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 creating problems involving addition and subtraction of two-digit numbers.

So, you're going to be writing some problems to match some equations.

Are you ready? Let's make a start.

We've got some keywords in our lesson.

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

So, I'll take my turn to say them and then it will 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 there are words that you know very well, but they're going to be useful in thinking about what sort of problem we are writing and solving in our lesson today.

So, look out for them as we go through.

There are two parts to our lesson today.

In part one, we're going to be creating addition problems, and in part two we're going to create subtraction problems. So, let's make a start with addition problems. And we've got Andeep and Izzy helping us in our lesson today.

The children decide to create some worded problems of their own, so they're going to write some problems. Andeep says, "First, you need to decide what your problem will be about." Izzy says, "I think I would like to write a problem about the books on the bookshelf." That's a nice idea, Izzy.

Andeep says, "Then you need to decide if it is an addition or a subtraction problem." Hmm.

What would you write? Izzy says, "I would like to write an addition problem.

Andeep says, "Addition can involve combining the parts to make the whole, so we can have one part and another part, and we can put them together to make the whole.

Or, he says, "We can have one part and increase that part to find the whole as well.

So, we might have two parts that we are combining or one part that we are increasing and adding to.

I wonder what sorts of problem Izzy's going to write.

Izzy says, "I will create a problem where I increase an amount." When I increase an amount.

I can tell a first then now story.

Have you come across first then now stories before when you've been thinking about addition and maybe subtraction as well? First, there were 71 books on the shelf.

Then 22 more books were put on the bookshelf.

Now, how many books are on the bookshelf? And did you see as Izzy built up her problem? You could see some books arriving on the bookshelf and you could also see a bar model being built up.

First there were 71 books.

That's one part.

Then 22 more books were put on the bookshelf.

That's another part.

How many are on the bookshelf now? That's the whole the bit we don't know.

We are going to solve 71 plus 22.

Izzy asks Andeep to solve her problem.

There's her problem again.

Andeep says, "I'm looking at the ones digits and they're going to sum to less than 10, so I will not bridge 10.

We've got a one and a two to add in the ones." He says, "I will partition both addends to solve." So first, he partitions them, then he adds the tens, 70 add 20 is equal to 90.

Then he adds the ones.

One add two is equal to three.

Now, he can recombine those parts.

90 plus three is equal to 93.

"There are 93 books on the shelf," he says.

He solved Izzy's problem.

Well done Andeep.

Now, Andeep writes a problem.

He says, "I will create an addition problem that combines two parts," so that other sort of addition.

Here's his problem.

I had 26 books and Izzy had 37 books.

We both put them on the bookshelves.

How many books did we put on the bookshelves altogether? And we've got some books appearing there.

I'm not sure we've exactly got 26 and 37, but we can see two sets of books being added together.

But we've also built our bar model.

One part is 26, that's Andeep's books, and the other part is 37, that's Izzy's books.

And we've got to combine them to find the total number of books.

26, add 37.

Have you spotted something? That's right.

The ones digits sum to greater than 10.

So, I'll need to partition one addend to solve because we're going to bridge through 10.

So, he's partitioning his 37.

So, 26 add 30 is equal to 56.

Now, we've got to add on seven and we can partition that into four and three to bridge through the multiple of 10.

56 add four is equal to 60, add another three is equal to 63.

So, there are 63 books on the shelf altogether.

Well done, Andeep.

Time to check your understanding.

Can you match the type of addition to the correct problem? Can you find a problem that is about combining the parts to make a whole? And another problem that is about increasing one part by another part to reach the whole.

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

How did you get on? Well, the problem with the stickers was about combining parts.

The teacher gave me 37 stickers and gave my friend 24 stickers.

How many stickers do we have altogether? So one person has 37, another person has 24, and they're going to take their two parts and they're going to combine them to make their whole.

What about the other problem? First I had 37 stickers and then my teacher gave me more stickers.

How many stickers do I have now? So, this time, I had 37 stickers and my teacher gave me 24 more.

So my number of stickers has increased.

So, this time I've increased one part by another part to reach the whole.

In the first problem, the parts can be combined in any order and they can in the second part as well.

But there's a definite order in the story.

First I had 37 and then my teacher gave me 24.

But we know that we can add the parts in any order and the sum will stay the same.

Andeep writes an equation and he asks Izzy if she can write a problem which this equation could represent.

So, he's got something is equal to 45 plus 34.

Can you see that the sum is written first in this equation? Izzy says, "It is an addition equation.

I think I will combine two parts to make the whole.

My problem will be about pencils," she says.

There were 45 pencils in the box and 34 pencils on the table.

How many pencils were there altogether? So she's combining the two sets of pencils to get her whole.

"The ones digits, she says, sum to less than 10, so I will not bridge 10.

I'm going to partition both addends to solve it." We haven't drawn a bar model this time.

I think we can picture those pencils.

45 in a box, 34 on the table and we're going to combine them to get our whole.

So, she's partitioned, then she's going to add the tens.

40 plus 30 is equal to 70.

Now, she can add the ones, four plus five is equal to nine.

And now she can recombine her tens and ones, 70 plus nine is equal to 79.

There were 79 pencils altogether.

Andeep uses the same equation and the same idea to write a different addition problem.

He says, "I think I will increase one part by another part to make the whole.

My problem will still be about pencils though," he says.

First, there were 45 pencils in the box.

Then, I put 34 more pencils in the box.

Now, how many pencils are in the box? Can you see? We've increased the number of pencils that were in the box.

He says, "I will solve it by partitioning one addend.

Okay, Andeep, off you go.

He's just going to partition the 34 and he's going to show us on a number line, 45 add 30 is equal to 75.

75 add four is equal to 79.

Of course, it's the same sum, isn't it? It's the same total.

But in his problem now, there are 79 pencils in the box.

Time to check your understanding.

Use the equation shown to write a problem that involves combining two parts to make the whole and then solve it.

Pause the video, have a go.

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

I wonder what your problem was about.

We wrote problem about sweets.

There were 58 sweets in a box and 24 sweets in a bag.

How many sweets were there altogether? So, we had some sweets in one place, some sweets in another and we were combining them to make a total.

I wonder what your problem was about.

We still need to solve the problem though, don't we? So, we can partition just one addend.

Can you see that our ones digits are going to bridge through 10? So, 58 add 20 is equal to 78.

And then, we can partition our four into two and two.

78 add two is equal to 80.

Add another two is equal to 82.

So, there were 82 sweets altogether.

Now, another check.

Can you use the same equation to write a problem that involves increasing one part by another part to make the whole? Pause the video, have a go.

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

So, what did you go for this time? We've stuck with the sweets fit.

This time, we've just thought about the sweets in the box.

There were 58 sweets in a box.

The shopkeeper put 24 more sweets into the box.

Now, how many sweets are in the box? So, this time we've increased the number of sweets in the box.

We don't need to solve the problem again because it can be solved in the same way for both types of problem.

It doesn't matter whether our problem is about combining or about increasing.

We can use the same addition strategies to solve it efficiently.

Time for you to do some practise.

For each of the equations below, you're going to write and solve two addition problems. So the first one you're going to write and solve combines two parts to make the whole.

And in the second problem that you write and solve, you're going to think about a problem that increases the first part to reach the whole.

And you've got four equations to use there.

So, pause the video, have a go at writing and solving those problems. And when you're ready for some feedback, press play.

How did you get on? I dunno what sort of problems you wrote, but these are some that we wrote.

So, we said for 34, add 25, there were 34 children in the hall and 25 children in the playground.

How many children were there altogether? So, this problem combines the parts to make the whole and we can partition both 'cause we're not going to bridge through 10.

20 plus 30 is equal to 50, four plus five is equal to nine, 50 plus nine is equal to 59.

So, there were 59 children altogether.

The other sort of problem we could have written would've been like this.

First, there were 34 children in the hall, then 25 more children went into the hall.

Now, how many children are in the hall? This problem increases one part by the other part to make the whole, but we don't need to recalculate because we know that our answer to our equation is going to be the same.

But this time, our answer is there are 59 children in the hall.

Let's look at B.

We've talked about building bricks in this problem.

There were 35 building bricks in the box and 24 bricks on the carpet.

Oh, dear, somebody hasn't tidied up.

How many building bricks were they altogether? So, we're going to combine the parts to make the whole.

30 plus 20 is equal to 50.

We've partitioned both our addends, and then the ones, five plus four is equal to nine.

50 plus nine is equal to 59.

Oh, do you notice, it's the same answer in A, we had 34 plus 25, and now in B we've got 35 plus 24.

We've got the same number of tens and ones.

We are just combining them in a slightly different order.

So, there are 59 bricks altogether.

And now for our increasing problem, first there were 35 bricks in my model.

Then I added 24 more bricks to my model.

Now how many bricks are in my model? This time, we are increasing one part to make the whole.

Now, there are 59 bricks on the model.

The same equation of course.

So you may have noticed that the sum in each equation was the same because the number of tens and ones in each equation was the same.

I think we spotted that, didn't we? Let's look at C.

58 add 23 there were 58 sheep in the field and 23 sheep in the barn.

How many sheep were there altogether? We are combining the parts to make the whole.

This time though, we're going to bridge through 10.

Eight plus three is greater than 10.

So, we are just going to partition the 23.

58 add 20 is equal to 78, and then we partition our three into two and one.

78 add two is equal to 80, and 80 add one is equal to 81.

So, our answer to our equation is 81, our sum is 81.

There were 81 sheep altogether.

Let's write an increasing problem.

First there were 58 sheep in the field, then 23 more sheep joined them in the field.

Now, how many sheep are in the field? This problem increases one part by the other to make the whole.

We don't need to recalculate, do we? 'Cause it's the same equation.

But now we can say there are 81 sheep in the field.

And let's look at D.

Ooh, do you notice anything about the numbers? 53 and 28? 58 add 23.

Hmm, I wonder what we're going to find.

There were 53 cars parked in the car park and 28 cars parked on the street.

How many cars were parked altogether? We are combining the parts to make the whole.

53 add 20 is equal to 73 and then we're going to partition our eight into seven and one.

73 add seven is equal to 80 and another one is equal to 81.

There were 81 cars parked altogether.

And another problem to do some increasing.

First there were 53 cars parked in the car park.

Then 28 more cars drove in.

Now, how many cars are in the car park? We've increased the number of cars in the car park.

There are 81 cars in the car park now.

What did you notice about those answers as well? Yes, the sum in each equation was the same because the number of tens and ones in each equation was the same.

It was just that we swapped it around.

The ones went with a different number of tens each time, didn't they? Well done.

I hope you had fun writing your own problems. Now, we're going to create some subtraction problems. Izzy says, "I will write another problem about books on a bookshelf." And Andeep says, "Subtraction can be partitioning one part from the whole to find the other part or decreasing the whole by subtracting one part to find the remaining part." So again, we can write different types of problems. Izzy says, "I will create a problem where I decrease the whole.

When I decrease the whole, I can tell a first then now story like we did with increasing the whole for addition." First there were 93 books on the shelf, then 22 books fell off the bookshelf.

Oh, dear, I hope there was nobody sitting on the floor by the bookshelf when they fell off.

So, our whole was 93 and 22 books have fallen off.

That's one of our parts.

Now, how many books are on the bookshelf? That's our missing part.

Izzy asks Andeep to solve her problem.

We've got 93, subtract 22.

He says, "When I subtract two from the 93, I will not bridge 10.

When we subtract, we partition one part to solve it, but we don't have to worry about bridging through 10.

So 93, subtract 20 and then subtract two.

93 subtract two first, this time is 91.

Subtract 20 is 71.

So our missing part is 71.

There are 71 books on the shelf.

Now, Andeep writes a problem.

He says, "I will create a subtraction problem that partitions one part from the whole." So, let's have a look at what his problem looks like.

There were 63 books on the bookshelf and I had read 37 of them.

How many of them had I not yet read? Oh, that's an interesting problem, isn't it? None of the books are going anywhere.

He's just sort of sorting them into two groups, the ones he's read and the ones he hasn't read.

So, those are our two parts.

63 is the whole, one part is the books he has read and the other part is the books he hasn't read.

And we know that to find a missing part, we subtract the known part from the whole, 63 subtract 37.

Or he says, "When I subtract seven from 63, I will cross the tens boundary, I will bridge 10.

And remember when we subtract, we just partition the part we are subtracting.

So, we're going to subtract our seven ones first, but we're going to partition our seven into three and four.

63 subtract three is equal to 60 and subtract the four is equal to 56.

So, we've subtracted seven altogether.

Now, we need to subtract the 30.

56 subtract 30 is equal to 26.

So, our missing part is 26.

And that's the number of books that Andeep has not yet read.

You've got a bit more reading to do Andeep, but you've read 37, that's a very good start.

Let's check your understanding.

Can you match the type of subtraction to the correct problem? So which problem is partitioning one part from the whole to find the remaining part and which problem is decreasing the whole by one part? Pause the video, have a look at the problems, and when you're ready for some feedback, press play.

How did you get on? So, in this problem there were 61 sweets altogether.

24 were in the tin and the rest were in the bag.

How many sweets were in the bag? So the sweets aren't going anywhere, but we've got our whole of 61 and we've put them into two parts, some in the tin and some in the bag.

And for our other question, first I had 61 sweets and then I ate 24 sweets.

Well, we've definitely decreased an amount there, haven't we? Some of the sweets have gone away because I've eaten them.

Now, how many sweets do I have? Well done.

I hope you were able to sort those problems out.

It's really useful to be able to spot different types of problem even if we solve them in exactly the same way.

Andeep writes an equation, he asks Izzy if she can write a problem which this equation could represent.

Something is equal to 79 subtract 34.

Izzy says it is a subtraction equation.

I think I will partition one part from the whole to find the remaining part.

"My problem will be about pencils," she says.

She says there were 79 pencils in the box.

34 of them needed to be sharpened.

How many pencils were already sharp? Ah, so there are 79 pencils.

She's spotted that our whole is not at the beginning of our equation this time.

34 of them need to be sharpened.

They've not gone anywhere have they? But 34 need to be sharpened.

How many pencils were already sharp? So, if we subtract the ones that need to be sharpened, we'll find out how many are already sharp.

She's going to solve it.

She says when I subtract four from nine, I will not bridge 10.

When we subtract, we can partition one part to solve it.

So, she's going to partition the 34 and subtract those parts from the 79.

And she says if she does that, 79 subtract 30 is equal to 49.

49 subtract four is equal to 45.

So, 45 pencils were already sharp.

She sold her own problem.

Well done Izzy.

Andeep uses the same equation and the same idea to write a different subtraction problem.

He says, "I think I will decrease the whole by one part to find the remaining part." So, he's going to write a decreasing problem, a sort of first then now problem.

"My problem will still be about pencils," he says.

First there were 79 pencils in the box, then I threw away 34, which were broken.

Now, how many pencils are in the box? Well, we've definitely decreased that amount by throwing some away, haven't we? He says, "I will solve this by partitioning the known part." 79 subtract 34.

He's going to show it on a number line.

79 subtract 30 is equal to 49.

Subtract another four is equal to 45, the same answer that Izzy got.

Now, there are 45 pencils in the box.

It's the same answer and we can use the same strategy to solve the subtraction.

But the problem is talking about a different way of thinking about subtraction.

Time to check your understanding.

Use the equation shown to write a problem that involves partitioning one part from the whole to find the remaining part and then solve it.

You might want to use pencils as well or maybe bricks like we used in the first part.

Pause the video, have a go, write a problem and solve it.

And then when you're ready for some feedback, press play.

How did you get on? We went with sweets.

There were 82 sweets in a box in the shop.

24 of them were in packets and the rest were in bags.

How many sweets were there in bags? So, all the sweets are in the box and we know how many were in packets and we want to work out how many of them were in bags.

So, we're going to subtract our known part 24 from our whole of 82.

We can partition our known part to subtract.

And we are going to bridge through 10 here, aren't we? 82 subtract 20 is equal to 62.

And then we can partition our four into two and two.

62 subtract two is equal to 60, subtract another two is equal to 58.

So, the answer to our subtraction is 58.

There were 58 sweets in bags.

Now, time to have another go.

Use the same equation to write a problem that involves decreasing the whole by one part to find the remaining part.

And if you're stuck for something to write about, maybe you could think about sweets again.

Pause the video, have a go.

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

What did you come up with this time? Yes, we stuck with the sweets again.

There were 82 sweets in the shop and the shopkeeper sold 24 sweets.

Now, how many sweets are there in the shop? Well, that number has definitely decreased, hasn't it? But we don't need to solve the problem again because it can be solved in the same way for both types of problem.

It's the same equation and we can use the same subtraction strategy to solve our problem.

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

For each of the equations shown A, B, C, and D, you are going to write and solve two subtraction problems. Your first subtraction problem is going to be one that partitions one part from the whole to find the remaining part.

And in your second one, you're going to write a problem that decreases the whole by one part to find the remaining part.

So, pause the video, write and solve your problems. And when you're ready for the answers and some feedback, press play.

How did you get on? So, for A, we had 59, subtract 24.

So, we could have written a problem like this.

There were 59 children in the hall, 24 of them were sitting on the floor and the rest were standing up.

How many children were standing up? So this problem partitions one from the whole to find the remaining part.

Part of the children are sitting on the floor and the other part are standing up.

We know that the known part is 24.

So, we're going to subtract that from the whole to find out how many were standing up.

And we can subtract our tens and our ones here.

We are not bridging through 10.

So, we are starting with the ones, 59 subtract four is equal to 55, subtract another 20 is equal to 35.

So, 35 children were standing up.

Let's think about another problem.

First, there were 59 children in the hall, then 24 children left the hall.

Now, how many children are in the hall? And this problem decreases the whole by one part.

We've decreased our whole by the 24 children who've left.

We don't need to recalculate though because we can use the same equation to calculate, but this time there are 35 children left in the hall.

And what about B? There were 59 building bricks altogether, 25 were in a box and the rest were on the carpet.

How many building bricks were there on the carpet? Oh, dear, somebody needs to tidy up and I hope nobody steps on them because they hurt when you step on them, don't they? So, in this problem, we've partitioned one part from the whole.

One part of the 59 building blocks are in a box, that's the 25.

And the other part that we don't know the number of is on the floor, on the carpet.

So, again, we can subtract to find the whole.

We are going to subtract the known part, which is the 25 in the box to find the missing part, the ones on the carpet.

This time, we're going to subtract our tens first.

59 subtract 20 is equal to 39 and 39 subtract five is equal to 34.

Well there are 34 bricks on the carpet.

Let's think about another problem.

First, there are 59 building bricks in my model.

Then I took 25 bricks from my model.

Now, how many bricks are in my model? We've decreased the number of bricks, haven't we? We don't need to recalculate, it's the same equation.

But this problem decreases the whole by one part to find the remaining part.

Now, there are 34 building bricks in the model.

Did you notice a link between the two calculations, the two equations? We had 59 subtract 24, and then we had 59 subtract 25.

One more was subtracted in the second equation than the first.

So, the remaining part was one less.

So, I wonder what problem you wrote for C.

We went with some sheep.

There were 81 sheep, 23 were in the barn and the rest were in the field.

How many sheep were in the field? So, this problem partitions one part from the whole.

The hole is 81 sheep.

We know that one part is 23 that are in the barn, the other part are on the field.

So, we can solve this by subtracting our known part from our whole.

We're going to bridge through 10 this time.

So we're going to partition our 23.

81 subtract 20 is equal to 61, and then we partition our three into one and two.

61 subtract one is 60, subtract another two is 58.

So, there were 58 sheep in the field.

We could write another problem about sheep to do a decreasing problem.

First there were 81 sheep in the field, then 23 left the field.

Now, how many sheep are in the field? This problem decreases the whole by one part to find the remaining part.

We don't need to recalculate.

We know that the answer is still 58.

This time though we can say there are 58 sheep in the field now.

And finally, for D, we went with cars.

There were 81 cars, 28 were parked in the car park and the rest were parked on the street.

How many cars were parked on the street? So again, we're partitioning our whole number of cars, 81 into the 28 in the car park and the unknown part that are on the street.

So we need to subtract and we're going to bridge through 10 again.

So we've subtracted our 20 to get to 61, and then we're going to partition our eight into one and seven to bridge through the multiple of 10.

61 subtract one is equal to 60, subtract another seven is equal to 53.

So, there were 53 cars parked on the street.

What about a problem where we reduced the number? First, there were 81 cars in the carpark, then 28 cars drove out.

Now, how many cars are in the carpark? So, this problem decreases the whole by one part to find the remaining part.

We don't need to calculate again.

We know that there are 53 cars now in the carpark because it's the same equation.

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

We've been creating addition and subtraction problems. So, what have we been thinking about? Well, we know that when creating problems, we must decide whether we want to create an addition or a subtraction problem.

Addition problems can involve combining two parts to make the whole, or increasing one part by the other part to reach the whole.

And subtraction problems can involve partitioning one part from the whole to find the other part or decreasing the whole by one part to find the remaining part.

I hope you've enjoyed creating problems in this lesson.

I've certainly enjoyed working with you and I hope I get to work with you again soon.

Bye-bye.