Lesson video

Hello there.

How are you today? My name's Ms. Coe and I'm really excited to be learning with you today in this unit on using knowledge of part whole structures to solve additive problems. If you're ready to get started, let's get going.

In this unit, we've been using our knowledge of part, part whole structures to think about additive structures.

And by the end of this lesson today, you will be able to say that you can use mental strategies and known facts to calculate the value of a missing part.

We have two key words for this lesson today.

I'm going to say them and I'd like you to say them back to me.

My turn, represent.

Your turn.

My turn, addend, Your turn.

Great job.

Let's think about what these words mean.

To represent something means to show in it a different way.

So for example, using part to part whole models or bar models to represent word problems. Addends are any numbers added together.

So in the equation, 3 plus 2 is equal to 5, 3 and 2 are the addends.

They're being added together.

This lesson today we'll be using mental strategies and known facts to calculate the value of a missing part and the lesson is split up into two cycles.

In the first cycle, we will be forming equations and in the second cycle we will look more closely at calculating efficiently.

So if you're ready to get going, let's get started with our first cycle.

In this lesson today, you're going to meet Aisha and Alex, and as always, they're going to be asking us questions and helping us with our learning.

So let's start here.

Year 6 are on a trip to a local theme park.

Have you ever been to a theme park? You might have rollercoasters there or different games for you to play.

One third of the pupils queued for the dodgems, half of them queued for the log flume.

How many queued for the rollercoaster? Hmm, I wonder how we're going to solve this one.

Aisha is going to use number rods to represent the problem.

She said that the orange bar represents all of the pupils, so all of the year 6 pupils at the local theme park.

She's going to use the light green rod to represent the pupils that are queuing for the dodgems. So we know that one third of the pupils are queuing for the dodgems. The yellow bar is going to represent the pupils queuing for the log flume.

We know that half of the Year 6 pupils are queuing for the log flume, so the yellow bar is half the length of the orange bar.

So Alex is absolutely right.

This means that the question mark represented in this bar model represents the pupil's queuing for the rollercoaster.

It is the part that we don't know, our unknown.

We can also write this as an equation.

So we can say that the orange is equal to the light green plus the yellow plus the red.

And remember the orange is our whole, the number of pupils.

The light green represents one third of those pupils.

The yellow represents half of those pupils and the red is our unknown.

It's the pupils who are queuing for the rollercoaster.

Take a closer look at our bar model representation now.

What do you notice? Hmm, well we still have the same worded problem.

We have a whole, we have one third, half, and an unknown, but what's changed this time is that we've given values to those different parts.

So in this bar model, the 48 represents all of the Year 6 pupils.

The 16 represents the pupils who are queuing for the dodgems, and the 24 represents the pupils who are queuing for the log flume.

We still have that unknown value which is represented by the red rod or the question mark, and that represents the number of pupils who are queuing for the rollercoaster.

We still don't know how many that is.

So let's think for a moment about what is the same and what is different about these representations here.

Well, the one on the left has used letters whilst the other one has numbers and we have a missing part or an unknown in both bar models.

Alex thinks that we could write an equation to work out the missing part.

What do you think? Could you write an equation to show how we could find the missing part? How could we represent these bar models as equations then? Well, we could find the missing part by subtracting twice.

So in the first model we could say that orange subtract light green subtract yellow, is equal to the red one, our unknown value.

And in the numerical bar model we could say that 48 subtract 16 subtract 24, is equal to the unknown.

Now we can do this because we know that the parts sum to the whole, they are equivalent, and so we could subtract the known parts from the whole to find the value of the unknown part.

That's one strategy to find that missing part.

Aisha thinks we have another way to do that.

We could represent the bar models as missing addend problems. So instead of using subtraction, we know that the orange rod is equal to the length of the light green rod and the yellow rod and the unknown.

So we can say that the light green rod plus the yellow rod plus the unknown is equal to the orange.

What would that look like numerically? Well, we could have 16 plus 24 plus something, our unknown, is equal to 48.

So when there is a missing part, we can write a repeated subtraction equation or we can write a missing addend equation.

They mean the same thing and they represent the same problem, but you might think that one is easier to think about than the other.

Time to check your understanding.

I would like you to write a repeated subtraction equation to represent this problem.

48 Year 6 pupils went on a trip to a local theme park.

This time 12 pupils went to the soft play, 20 pupils went on the pirate ship, the remaining pupils went on the carousel.

How many pupils went on the carousel? So I'd like you to write a repeated subtraction equation to represent this and you have the bar model there to support you.

Take a moment to have a think.

Welcome back.

How did you get on? So remember, in a repeated subtraction equation, we start with the whole.

In this case that's 48 and we are subtracting our known parts.

So 48 subtract 12 subtract 20 is equal to our unknown part.

Well done if that's the equation that you wrote.

This time, I would like you to write a missing addend equation to represent the problem.

So the problem is the same, the unknown part is still the same, but this time I would like you to represent it as a missing addend equation.

Take a moment to have a think.

Welcome back.

How did you get on? Did you think carefully about what was the same and what was different in the two equations that you were writing? So with a missing addend equation, we start with the parts and we're adding them up and we know that the parts are equivalent to the whole.

So we should have written 12 plus 20 plus something is equal to 48.

Now remember you may have written the parts in a different order and that's absolutely fine.

Addition is commutative, which means we can add the parts in any order to make the same whole.

Time for your first practise task.

I would like you to represent the following problems as a repeated subtraction and missing addend equation.

So for example, question one says, Alex has 65 pounds to spend.

He buys a packet of cards for 4.

99 pounds and a book for 15 pounds.

How much money does he have left to spend? So remember we're going to write two different equations to represent that problem.

If it helps you to draw a bar model to represent that problem as well, that's absolutely fine.

So you have a second question there as well, and then you have question three to think about too.

Pause the video here, think carefully about those worded problems. I'll see you shortly for some feedback.

Welcome back.

How did you get on? Did you think really carefully about how to represent these worded problems in two different ways? So let's take a closer look at number one.

Alex has 65 pounds to spend.

He buys a packet of cards for 4.

99 pounds and a book for 15 pounds.

How much money does he have left to spend? If we think about this in terms of the whole and the parts, the whole is 65 pounds.

That's the amount that he has to spend.

And we have three parts.

One part is 4.

99 pounds, which represents the packet of cards that he bought.

One is 15 pounds, which is the book, and the final part is unknown.

It's the money that he has left.

So we think about it in terms of parts and wholes.

We can use this to write a repeated subtraction equation.

We start with the whole.

So we have 65 pounds, subtract 4.

99 pounds subtract 15 pounds, is equal to the amount of money that he has left.

Or if we want to think about it as a missing addend equation, we know that the three parts are equal to the whole.

We know the whole is 65 pounds, so we can say that 15 pounds plus 4.

99 pounds plus something is equal to 65 pounds.

For question two, Aisha goes to her gymnastics lesson for two hours.

She spends 45 minutes practising her floor routine.

Then she spends 35 minutes on the trampolines.

She spends the remaining time practising her vault.

How long does she practise the vault? Now you can see in these equations that I've used the number 120.

Where did that come from? Well, I thought about the mixed units that I have here.

We have two hours, but then the parts are in minutes.

So it may be easier sometimes to convert so that they're all in the same unit of measure.

I know that one hour is equal to 60 minutes, so two hours is equal to 120 minutes.

So I can represent this problem as 120 subtract 45 subtract 35 is equal to the missing part, which is how much time she spends practising the vault.

Or I can write it as a missing addend equation, 45 plus 35 plus something is equal to 120.

For question three, you may have noticed yet another unit of measure.

So this time we're thinking about mass, but remember it doesn't matter about the context of the worded problem.

We can still represent them as repeated subtraction and missing addend problems. Alex is pouring flour into a bowl.

He needs 1.

2 kilogrammes altogether.

After the first pour, he has 0.

5 kilogrammes.

For his second pour, he pours in another 350 grammes.

How much more does he need to pour on his third pour? So this time I've kept the kilogrammes and grammes, but you may have changed these as well into all grammes or all kilogrammes.

So I can write 1.

2 kilogrammes, subtract 0.

5 kilogrammes subtract 350 grammes, is equal to something which is our third pour.

Or I can write 0.

5 kilogrammes plus 350 grammes plus something is equal to 1.

2 kilogrammes.

Well done if you represented all three worded problems in two different ways.

Let's move on to the second cycle of our lesson where we are thinking about how to calculate efficiently.

Let's return to our problem from earlier.

48 Year 6 pupils are on a trip to the local theme park.

16 pupils queued for the dodgems, 24 pupils queued for the log flume.

How many pupils queued for the rollercoaster? Now we know that we can write this problem in two different ways.

We need to find the missing part and we can write that as 48 subtract 16 subtract 24 is equal to something, or we can write 16 plus 24 plus something is equal to 48.

We've got two different ways, therefore, of working out how many pupils queued for the rollercoaster.

Aisha is going to subtract each part one at a time.

So she's going to say 48 subtract 16 which is equal to 32.

Then she's going to do 32 subtract 24 which is equal to 8.

So she now knows that 8 pupils queued for the rollercoaster.

The missing part is 8.

And that's one strategy to find that missing part.

Alex, however, is going to use the missing addend equation to work out the problem because he says that he prefers adding together the known parts first and then subtracting them from the whole.

And that would also work too.

If we look at the bar model, we can imagine combining the parts that we know and then we just need to subtract that larger part from the whole to find the missing parts.

So Alex is going to do 16 plus 24 is equal to 40 and I can see a number pair to 10 there that would help me calculate really efficiently.

Then he's going to do 48 subtract 40 which is equal to 8.

So he agrees with Aisha, 8 pupils were queuing for the rollercoaster.

They've both got the same answer but they've worked it out in different ways.

So which strategy did you prefer? Did you prefer Aisha's strategy where she started with the whole and subtracted each part in turn to find the missing parts? Or did you prefer Alex's strategy where he added up the known parts first and then he subtracted that from the whole? Hmm, I think it really depends on the numbers and how confident you're feeling.

If you look closely at the numbers and feel that they'd be easy to subtract one at a time, then it might be more efficient to do it that way.

However, I think in this case, using our pair to 10, we can see that 16 plus 24 is equal to 40.

I personally found that much easier to subtract from 48.

Let's take a look at a slightly different problem.

We still have 48 Year 6 pupils who are going on their trip to the local theme park.

This time, 7 pupils went on the Devil's Drop.

That sounds scary.

12 pupils went on the Driving School, 8 pupils went on the spinning caps and the rest went on the train ride.

How many pupils went on the train ride? What do you notice about this problem? How is it different from our last problem? Well, that's right.

This time we have three known parts and one unknown parts, so we have four parts altogether.

But remember those four parts are still equivalent to, equal to, the whole and we've represented the problem as a bar model.

Aisha recognises that there are two equations that we could write.

We could say 48 subtract 7 subtract 12 subtract 8 is equal to the missing part, the number of children who went on the train ride.

Or, remember we could write this as a missing addend equation, 7 plus 12 plus 8 plus the unknown is equal to 48.

And remember that these two show two different ways to find out that missing part.

I wonder which one you would prefer? So Aisha recognises that actually this time, because there are three parts to subtract, it might actually be easier to add those parts together first.

And I think that makes sense.

I think if we're subtracting several parts, it can be quite tricky to keep track of where we're up to.

So we can do 7 plus 12 plus 8.

Remember that we can add these numbers together in any order that we like because addition is commutative.

I wonder if you can spot a quick and efficient way to sum these numbers.

So Aisha has spotted a number bond, 8 plus 12 is equal to 20, so she can add those two parts first.

Then we need to add 7 more.

Well we know that 20 plus 7 is 27.

So we now have the sum of the three parts and you can imagine that on the bar model as one big part with just that unknown part still.

And we know that 27 and something is equal to 48, so we can do 48 subtract 27 which is equal to 21.

We know that the missing part, the number of pupils that went on the train ride is 21 and we could check if we wanted to because if those four parts add up to the whole, which is 48, it means we're absolutely right.

And I agree Aisha, it was easy enough to think about it that way.

Time to do a quick check for understanding.

Solve the problem using either strategy.

48 Year 6 pupils are on a trip to the local theme park.

12 went to the soft play, 20 pupils went on the pirate ship, the remaining pupils went on the carousel.

How many pupils went on the carousel? So you can work out the missing part using either strategy.

Take a moment to have a think.

Welcome back.

Which strategy did you use? For this one, there are two known parts and one unknown part and we have 12 and 20 as the known parts, which are quite easy numbers to work with, I think.

You can start with 48, and remember, you can subtract the parts in either order.

So I would do 48 subtract 20 which is 28, and then 28 subtract 12.

Or you could add those two parts first.

So 12 plus 20 which is 32, and then subtract them from 48.

Either way, there were 16 pupils on the carousel.

The missing part is 16.

Time for your second practise task.

For your first question, I would like you to group the bar model by which strategy it would be best to use to solve the problem.

So remember the strategies that we've looked at are the repeated subtraction strategy where we subtract each part separately from the whole, or the adding known parts first strategy where we sum the known parts and then subtract that from the whole.

You might decide that some of them could be equally efficient to using either.

So you have seven bar models there to think about.

Look really carefully at the whole and the parts and think about the relationship between them to help you.

For question two, I would like you to solve the following worded problems. Remember, you might like to draw a bar model and you might like to represent them using those two different equations before you think about how to solve them.

So for A, Alex has 65 pounds to spend.

He buys a packet of cards for 4.

99 pounds and a book for 15 pounds.

How much money does he have left to spend? Which strategy would you find easier to solve that problem? You also have B and C to think about.

Pause the video here, have a go at those two questions and I will see you shortly for some feedback.

Welcome back.

How did you get on? Now remember, when we're thinking about efficiency, it can quite often be a personal thing.

I've organised the bar models into the way I would find most efficient, but it's okay if you have chosen a slightly different approach.

Let's take a look at some of them.

So in the repeated subtraction column, for example, I have got 60 and the parts of 20, 30, 5, and something I don't know.

I feel this would be useful for repeated subtraction because I'm subtracting multiples of 10 to start with.

I know that 60 subtract 30 is 30, subtract another 20 is 10, subtract 5 is 5.

I can do that quickly and efficiently without having to add the parts first.

In the adding known parts first column, I have the same whole of 60, but I have 38 plus 15.

Now while I can subtract 38 from 60 mentally, I find that quite tricky because there'd be some regrouping.

I would much rather add together 38 and 15 and I can use my number bonds there or I can use my make 10 strategy.

So I know that 38 plus 2 is 40, so that gives me 40 plus 13, and then I can subtract that from the whole.

I also noticed that when I added those two parts together, the sum of those two parts was very close to the whole, so it made that subtraction a bit easier.

For either category, something like 60 subtract 5 subtract 5 subtract 2 is equal to something, is something that we could do either way.

I think it would be just as efficient to subtract two lots of 5 and a 2 from 60 as it would be to subtract 12 from 60.

Remember that you might have preferred a different strategy and that's absolutely fine.

I hope you thought about them really carefully and reasoned, perhaps with a friend, about why you placed them where you did.

Let's look at question two.

For two A, we had Alex and his money.

So remember that he spent 4.

99 pounds and then he spent a further 15 pounds and we were asked how much he had left to spend.

For this one, personally, I would add together the parts first.

I would do 15 pounds plus 4.

99 pounds, which I knew is 19 pounds and 99 pence.

No regrouping there, nice and easy to add together.

And then I would do 65 pounds, subtract 19 pounds and 99 pence.

I know that 19.

99 pounds is super close to 20 pounds, so I would've used an adjusting strategy here to find the missing part, which is 45 pounds and 1 penny.

Alex had 45 pounds and 1p left to spend.

Let's look at question two.

We spoke earlier about the importance, sometimes, of changing those units, so we could have thought about two hours as 120 minutes, which makes it a little bit easier to calculate.

So this time I used a repeated subtraction strategy.

You might have added together 45 and 35 and then subtracted from 120, and that's absolutely fine.

But either way, we had 40 as our missing part, which meant that Aisha spent 40 minutes practising the vault.

And for question C, Alex was pouring his flour.

So again, we had mixed units here, so I decided to think about decimals.

I knew that 350 grammes was equal to 0.

35 kilogrammes.

And so here I might use a repeated subtraction strategy.

Again, you might have added the two parts together and then subtracted 0.

85 from 1.

2.

You may also have converted all of this into grammes, and so working with four and three digit numbers instead, and that's absolutely fine.

The missing part was 0.

35 kilogrammes or 350 grammes, and that was how much he needed for his third pour.

Well done if you worked out all of those and thought really carefully about what the most efficient strategy for you was.

We've come to the end of the lesson where we've been thinking about using mental strategies and known facts to calculate the value of missing parts.

Let's summarise what we've learned.

You can represent a missing parts problem as a repeated subtraction equation or a missing addend equation.

And we thought really carefully about how both of those representations can help us to calculate.

So you can find that missing part either by subtracting each known part from the whole or by adding the known parts together and then subtracting from the whole.

And again, we've been thinking a lot about which of those might be more efficient depending on the numbers and the circumstance.

Thank you so much for your hard work today and I look forward to seeing you again soon.