Lesson video

Hello, my name's Mrs. Hopper, and I'm really looking forward to working with you in today's maths lesson.

It's from our unit adding and subtracting ones and tens to and from two-digit numbers.

So we're going to be looking at two-digit numbers, and we're going to be thinking about adding and subtracting and hopefully using our known facts to help us.

So if you're ready, let's make a start.

So in this lesson, we're going to be using number facts to solve addition and subtraction problems. So are you ready to solve some problems? Let's get going.

We've got three keywords in our lesson today.

We've got efficiently, whole, and part.

So I'm going to say them and then you can repeat them.

Are you ready? My turn, efficiently.

Your turn.

My turn, whole.

Your turn.

And my turn, part.

Your turn.

Excellent.

You might understand what those words mean, but they're going to be really useful to us, so look out for them as we go through our lesson today.

There are two parts to our lesson.

In the first part of our lesson, we're going to be combining and partitioning, and in the second part of our lesson, our problems are going to be about increasing and decreasing an amount.

So are you ready to solve some combining and partitioning problems? Let's get started.

And we've got Alex and Sam helping us with our learning today.

So we can use known number facts to help us to solve problems, and you might have been doing that already.

So let's think about that as we go through this lesson, thinking about using number facts that we know to help us to solve new problems. So let's look at this one and think about how we can represent it.

Sam bought a drink for 45 p and a straw for 4 p.

How much did she spend altogether? Well, let's represent it on a bar model.

You may have a good idea already or you may think you know what to do, but let's look at it on a bar model 'cause it's always really important to understand what the problem is telling us to do and what each item represents.

So Sam bought a drink for 45 p and a straw for 4 p.

So those are our two parts, and what we need to find out is the whole, and the bar model shows that.

45 p is a part and 4 p is a part, and to find the whole, we add the parts.

Part plus part is equal to whole.

So we need to calculate 45 p plus 4 p is equal to something.

Now, what about those known facts? Which known addition fact should be used to solve this efficiently? So efficiently means quickly and carefully, getting us the right answer in a quick way that draws on the things that we know already.

So what do you know already that could help you here? Well, Sam says, "I will partition the 45 p, so I can see the tens and the ones." So she's used the coins.

So she's got the 40 is four tens, four 10 ps in this case, and the 5 p is five 1 ps.

And she says, "I know I have to add 4 ones, or 4 p." So she's added those ones in as well.

She says, "I can see that there are five 1 p coins and four 1 p coins, and I can use the known fact 5 plus 4 is equal to 9." So she says, "I know 5 p plus 4 p is equal to 9 p.

So I know that 45 p plus 4 p is equal to 49 p." So the drink and the straw must have cost 49 p altogether.

Okay, so let's have a look at this problem in another way.

Sam bought a drink and a straw.

She spent 49 p altogether.

We've just worked that out, haven't we? The straw cost 4 p.

How much did the drink cost? Well, you might remember, but let's think about how the bar model would look different for this problem.

So, "Altogether I spent 49 p," says Sam.

49 p is the whole this time.

So there's our whole, and we know that it's a drink and a straw.

The straw cost 4 p.

So 4 p is a part.

So there's our part.

The drink is the other part, and that's the bit that we're trying to work out the cost for.

Even if you can remember it from the previous slide, let's imagine we don't know it.

How would we calculate it? So there's our drink, so many pence.

We don't know.

Well, it's a missing part, isn't it? So our drink is a part.

So to find a missing part, we subtract the part we know from the whole.

So whole subtract part is equal to part.

So the drink and the straw subtract the cost of the straw will give us the cost of the drink.

49 p subtract 4 p will be equal to the price of the drink.

So how much did the drink cost? 49 p minus 4 p.

That's what Sam says she needs to solve.

So which known fact will help her this time? Well, she's got 9 p there minus 4 p, and she knows that 9 minus 4 is equal to 5, and we can see that with the coins, which she's imagined them a little bit as if they were in a 10 frame there.

And then we know that the 40 doesn't change because we're only subtracting 4 p from the 9 p.

So that 40 will stay the same.

So it must be 45 p.

The drink cost 45 p.

We subtracted the 4 p from the 49 p, and we were left with 45 p.

I wonder if you can think what the final way of looking at this will be.

Sam bought a drink and a straw.

She spent 49 p altogether.

The drink cost 45 p.

How much did the straw cost? So, "Altogether I spent 49 p.

49 p is the whole." So there it is, the drink and the straw together.

This time, we know that the drink cost 45 p.

So 45 p is a part.

The other part is the straw, and we don't know how much that cost.

So how would we go about calculating this? We may know the answer, but it's always useful to think about how we would calculate if this was the missing part.

Well, we know that part plus part is equal to whole.

So we know that the drink plus the straw is equal to the total cost.

So this time, we've got 45 p plus something is equal to 49 p.

And sometimes if the difference is a small amount, then we can think about it as an addition.

So how much did the straw cost? 45 p plus something is equal to 49, and that's what Sam realises she needs to solve.

So 45 p plus something is equal to 49 p, and we can represent that on a number line.

"Which known fact will help me?" she says.

Well, she knows that 5 p plus 4 p is equal to 9 p and that the 40 doesn't come into it really.

It's just there.

It doesn't change.

So we know that 45 p plus 4 p must equal 49 p.

The straw cost 4 p.

And you can count on to find a missing part, and we call this the difference.

So can you see on the number line, Sam knew she had to count on from 45 up to 49 to find the cost of the straw, and she knew that that number fact, 5 plus 4 equals 9, could help her to work out the difference, and the difference was the cost of the straw.

So we've looked at that problem in three different ways, haven't we? Okay, time to check your understanding, thinking about those different ways that we can represent the problem.

So can you draw a bar model for each problem to find the whole and the parts and identify what we know and what is missing? Pause the video, have a go, and when you're ready, we'll get together and compare our bar models.

So how did you get on? So for the first one, we knew that there were 42 pens and 4 rubbers on the table.

How many items were on the table altogether? So our parts were 42 pens and 4 rubbers, and we had to combine them to find our whole.

The whole was unknown this time.

What about the next one? Altogether there were 46 items on the table.

Ah, so this time, we knew the whole, the altogether part, so we knew the whole.

4 were rubbers.

How many were not rubbers? So it was one part that we didn't know this time, and then for the final one, there were 44 items on the table.

When more were added, there were 46 items. Ooh.

So the 44 we might have thought was our whole, but actually, it was a part.

So there were 44 items on the table, and when more were added, we don't know how many more, there were 46 altogether, so how many items were added? So again, our missing number was a part this time.

I hope you were successful in drawing those bar models.

Another check.

Once you've got your bar models, can you match the problem to the known fact that you would use to solve it? So pause the video.

See if you can match the bar models to the known fact and the equation that would solve it, and then when you're ready, we'll get together for some feedback.

What did you think? So when we needed to combine the parts to make the whole, we needed to do 42 plus 4, and 2 plus 4 is the known fact that would help us.

The 40 isn't going to change because we're just adding those other one-digit numbers within 10.

What about the next one? Well, this time, we had to do a subtraction, didn't we? We had to subtract our known part from the whole, so 46 subtract 4.

So 6 subtract 4 equals 2 was the known fact that would help us.

And what about the next one? This was that finding the difference one, wasn't it, counting on.

So we needed to do 44 plus something is equal to 46, and if we knew that 4 plus 2 is equal to 6, then we knew that 44 plus 2 was equal to 46.

Well done if you matched those correctly.

Time for you to do some practise now.

So for question 1, you're going to draw a bar model and then write an equation to represent each problem, and the problems there, A, B and C, are underneath.

And then for question 2, you're going to write the known fact that you used to solve the problem.

So you're going to draw the bar models, and then you're going to write an equation to represent the problem.

Think about the known fact that you'd use and solve the problem.

So pause the video.

Have a go at representing and solving those problems, and when you're ready, we'll get together for some feedback.

How did you get on? So for a, the children spent some money.

Sam spent 4 pounds and Alex spent 21 pounds.

How much did they spend altogether? So here, we were combining the parts to make the whole.

So one part was 21 pounds and the other part was 4 pounds.

So we need to write an addition equation, 21 plus 4 is equal to something, and I know that 1 plus 4 is equal to 5.

So I know that 21 plus 4 must be equal to 25.

So the amount they spent altogether was 25 pounds, and the known fact I used was 1 plus 4 is equal to 5.

So for b, Sam spent 4 pounds, and Alex spent a different amount.

Altogether they spent 25 pounds.

So this time we knew the whole and one part, and the part was a small part so we could take it away.

So we need to write a subtraction equation, whole minus part is equal to part, 25 minus 4 pounds is equal to.

So there are 5 ones and 4 ones are subtracted, so the known fact we'd use would be 5 subtract 4 is equal to 1.

So I know that 5 subtract 4 is equal to 1.

So I know that 25 subtract 4 must be equal to 21.

So the missing part is 21 pounds.

Alex spent 21 pounds.

And for c, we need to find a difference here.

It's that little bit that's missing, isn't it? So Sam spent some money and Alex spent 21 pounds, and together they spent 25 pounds.

So this time we know Alex's part and we know the whole.

So this time we need to know what we'd need to add to 21 to equal 25.

So 21 plus something is equal to 25, and if we know that 1 plus 4 is equal to 5, we know that 21 plus 4 is equal to 25.

So Sam must have spent 4 pounds.

And on into the second part of our lesson.

This time, we're going to be thinking about increasing and decreasing an amount in our problems. So Alex has some pencils.

So first, Alex had 32 pencils.

Then he found another 3 pencils.

How many pencils does he have now? Well, let's represent this on a bar model.

So 32 is a part.

That was the part he had first, and then he found 3 more pencils.

So 3 is another part.

So what we don't know is the whole.

Part plus part equals whole.

So we need to do 32 add 3 to find out the whole number of pencils that he has now.

So which known fact should Alex use to solve this efficiently? Let's have a think.

He says, "I'll partition 32, so I can see the tens and the ones." So 32 is 3 tens and 2 ones.

"I now know I have to add 3 ones," he says, 2 ones plus 3 ones, "And I can use the known fact 2 plus 3 is equal to 5." I know that 2 plus 3 is equal to 5.

So 32 plus 3 must be equal to 35.

So Alex has 35 pencils now.

What about this one? Is this an addition or a subtraction equation? Let's have a look.

First, Alex had some pencils.

Then he found 3 more pencils.

Now he has 35 pencils.

How many did he have to start with? Well, let's think about this with a bar model.

So first, Alex had some pencils, and we don't know how many.

Then he found 3 more, and now he has 35.

Ooh.

So now he has 35.

35 pencils is the whole.

3 of those pencils were found, so 3 is a part, and the other part is the pencils he had at the beginning, and we don't know how many he had there.

So to find a missing part, we can subtract the whole we know from the part.

So 35 subtract 3 is equal to the number of pencils he started with.

He says, "I'll partition the 35, so I can see the tens and the ones." So 35 is 3 tens, 30, and 5 ones, 5.

He says, "I can see that there are 5 ones and I must subtract 3 ones." He says, "I can use the known fact 5 subtract 3." I know that 5 subtract 3 is equal to 2.

So I know that 35 subtract 3 must be equal to 32.

So Alex must have had 32 pencils to start with.

Right, so first, Alex had 35 pencils.

Then he put some pencils away, and now he has 32 pencils.

How many pencils did he put away? Hmm.

Let's draw a bar model to understand the problem first.

So first, Alex had 35 pencils.

So that was our whole.

Then he put some pencils away, and he had 32 pencils left, so 32 is a part, and the number he put away is the other part.

That's the part we don't know.

So 35 is more than 32, and 32 is less than 35.

So the missing part is the difference between them.

So there's 32 and 35 on the number line, and the difference is between them, and we could count either way.

So we could say 32 plus something is equal to 35 or we could say 35 minus something is equal to 32.

Two different ways to work out this missing number.

So let's think about the addition way.

What's the difference between 35 and 32? 32 plus something is equal to 35.

Well, there are 2 ones in 32.

So to reach 35, I must add 3 ones because we know that 2 plus 3 is equal to 5.

2 plus 3 is equal to 5.

So I know that 32 plus 3 must be equal to 35.

So the number of pencils that he put away is 3.

What about if we thought about it with subtraction though? 35 subtract something is equal to 32.

There are 5 ones in 35.

So to reach 32, I must subtract 3 ones.

I know that 5 subtract 3 is equal to 2.

So I know that 35 subtract 3 will be equal to 32.

So whichever way we work it out, that number of pencils he put away was 3 pencils.

Right, time to check your understanding.

Can you match each problem to the known fact you would use to solve it? You might want to draw a bar model to help you or you might be able to visualise the bar model.

Pause the video, have a go, and when you're ready, we'll get together for some feedback.

How did you get on? Did you spot that two were the same this time? Hmm.

So let's start with this one first.

So this problem was, first, there were 38 children in the room, and then some children left, and now there are 36 children in the room.

So if we looked at the ones, we knew we were going from 38 to 36.

So 38 subtract something would equal 36, and 8 subtract 2 is equal to 6.

So 38 subtract 2 is equal to 36.

So that was one of those finding the difference ones, but we thought about it with subtraction.

For this problem, first, there were 32 children in the room, and then 6 more came in.

Well, we knew a part and a part.

So we had to combine them to make the whole.

So 2 plus 6 is equal to 8.

So 32 plus 6 must be equal to 38.

So was the last one the same then? Let's have a look at the problem.

First, there were some children in the room, and then 6 children came in.

Now there are 38 children in the room.

Ah.

So this time, we knew a part, the small part, and we knew the whole was 38.

So if we knew that 2 add 6 is equal to 8, we knew that 32 add 6 would be equal to 38.

So we could use that known fact to solve that problem.

Well done if you got those right.

Time for you to do some practise.

You're going to draw a bar model and then write an equation to represent each problem, and then you're also going to write the known fact that you used to solve it.

So pause the video.

Have a go at solving these three problems, and then when you're ready, we'll get together for some feedback.

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

So first, Sam had 76 stickers on her chart.

Then she found 3 more.

How many stickers does she have now? So we're combining the parts here to make a whole, 76 and another 3 to make our whole.

So 76 add 3 is our addition equation, and there are 6 ones added to 3 ones.

So we could use the known fact 6 plus 3 is equal to 9.

So if we know that, then we also know that 76 plus 3 must be equal to 79.

So Sam now has 79 stickers in her chart.

Now this time, first, Sam had some stickers on her chart, and then she found 3 more, and now she has 79.

So this time, the whole was 79, and we knew that one part was 3.

So to find the other part, we can subtract the part we know from the whole.

So we need to write a subtraction equation.

79 subtract 3 is equal to our missing part.

Well, there are 9 ones and 3 are subtracted.

So we can use the known fact 9 subtract 3 is equal to 6, and if we know that, we know that 79 subtract 3 must be equal to 76.

So the number of stickers she had to start with was 76.

And what about c? First, Sam had 79 stickers on her chart, and then she lost some, and now she has 76 stickers.

How many stickers did she lose? So again, we need to find the part that was subtracted.

This time, we can think about the difference.

79 subtract something is equal to 76.

There are 9 ones, and when some are subtracted, there are 6 left.

So we could use the known fact that 9 subtract something equals 6, and we know it's 9 subtract 3 equals 6.

So we know that 79 subtract 3 must be equal to 76.

So she must have lost 3 stickers, but we could also have thought of this using addition.

We could have said 76 plus something is equal to 79.

So then we could have thought of 6 plus something is equal to 9, and we know that 6 plus 3 is equal to 9.

So 76 plus 3 must have been equal to 79.

So we know that that missing number is 3 and that Sam must have lost 3 stickers again.

Well done if you got those right, and we've come to the end of our lesson.

We've been learning about using number facts to solve addition and subtraction problems. What have we learned? We've learned that you can use known facts to help find new facts efficiently.

You can use known facts to solve addition and subtraction problems, and you can draw bar models to help represent and understand the problems. It's been really useful to help us to find out which equation we're trying to solve and then to find the known fact that will help us to solve that equation.

Thank you for all your hard work and your thinking today.

I hope you've enjoyed it as much as I have, and I hope I get to see you again soon.

Bye-bye.