Lesson video

Hello there, my name is Mr. Goldie and welcome to today's maths lesson.

And let's look at the lesson outcome.

So the lesson outcome is, I can solve multi-step addition and subtraction problems efficiently.

Let's look at those keywords.

So I'm going to say each keyword, can you repeat it back? The first keyword is efficient.

And the next keyword is reorder.

Let's take a look at what those words mean.

Efficient means not wasting time or effort.

It means working quickly in an organised way.

And reorder means arrange something in a different way.

And here's our lesson outline.

So the first part of the lesson is rearranging problems and the second part of the lesson is calculating with addends and subtrahends.

Let's get started.

And in this lesson you will meet Lucas and Izzy who are going to be helping you with your maths and working through some difficult problems with you.

So Izzy and Lucas are solving multi-step problems. So these are problems with more than one step.

There are 16 people on a bus.

There's our bus with 16 people on it.

At the next stop, three people get on the bus and six people get off.

And there's three people getting on the bus and six people getting off the bus.

"What's the most efficient way to solve the problem?" asks Izzy.

"Should we reorder the problem?" ask Lucas.

So there are two different ways you could calculate the answer to this problem.

You could do 16 add three, subtract six, or you could do 16 subtract six, add three.

They would both give the same answer.

I wonder what the most efficient way of solving the problem is.

And remember, efficient means solving the problem in a quick and organised way.

Izzy and Lucas represent each calculation using tens frames.

So we've got the calculation 16 and three, subtract six, and Izzy says I'm going to start with 16 and add three.

So here's 16 represented in the tens frames.

Izzy adds three and then she says, "Now I'm going to subtract six." So Izzy now subtracts six.

And that gives us the answer 13.

And next, let's have a go at the calculation, 16 subtract six, add three.

"I'm going to start with 16 and subtract six," says Lucas.

Here's 16 and Lucas subtracts six.

There are 10 left.

"Now I'm going to add three," says Lucas.

Lucas adds three back on.

The answer is 13.

It's the same answer, because of course the steps are the same.

In both calculations, we're starting with 16, we're adding three and we're subtracting six.

But which order is more efficient? Which order is easiest to calculate? So here's 16 add three, subtract six.

Let's break it down into 16 add three, that equals 19.

And the 19 subtract six equals 13.

The answer is 13.

Let's have a look at 16 subtract six, add three.

So 16 subtract six equals 10, and then 10 add three equals 13.

So which one is easiest.

Izzy and Lucas think it is 16 subtract six, add three.

I think it's much easier to subtract six first.

16 subtract six is easy to calculate, because it counts back to a multiple of 10.

10 add three is also easy, because it counts on from a multiple of 10.

Choose the order that is more efficient to calculate.

So anytime you're faced with a calculation similar to these ones, look really carefully at those numbers.

See if it's easier to reorder the calculation to make it more efficient to calculate.

Izzy and Lucas look at these problems. They've got four problems there.

"What's the most efficient way to solve each problem? Should we reorder the problem or solve it as it is," says Lucas.

They start with the first problem.

So let's start with 222 subtract two, add 15.

Is it best to keep the same order or is it better to reorder the problem? "I don't think we should reorder the calculation," says Izzy.

222 subtract two equals 220.

"220 add 15 is quite easy too," says Lucas.

220 add 15 equals 235.

So the answer is 235.

So for that first calculation, Izzy and Lucas don't think they should reorder it.

Izzy and Lucas look at the next problem.

So this time they're looking at the problem, 117 add 15, subtract 17.

"I think we should reorder the calculation," says Izzy.

So Izzy thinks they should reorder it into 117 subtract 17, add 15.

That will of course give the same answer.

All we've done is reorder the steps.

The answer itself won't to be any different.

"Let's start with 117 subtract 17," says Lucas.

"117 subtract 17 equals 100," says Izzy.

It's easy to add 15 to 100, 100 add 15 equals 115.

So the answer there is 115.

So it's much easier to reorder the calculation, because of the numbers involved.

Izzy and Lucas look at the next problem.

So the next problem is 290 add 10, subtract 99.

"I don't think we should reorder the calculation," says Izzy.

"You're right, Izzy," says Lucas.

"Let's start with 290 add 10, because it equals a multiple of 100." So 290 add 10 equals 300.

To subtract 99, we can subtract 100 and add one.

300 subtract 100 add one equals 201.

So 300 subtract 99 equals 201.

So the answer there is 201.

How would you answer the last problem? So the last problem is 96 subtract seven, add four.

How would you work out the answer? Look very, very carefully at those numbers.

Should you reorder the calculation or should you leave it as it is? Pause the video and have a go at trying to work out the answer to that last problem.

And welcome back.

Did you manage to find the answer? Did you reorder the calculation? Let's have a look to see what you should've done.

So Izzy says you should reorder the calculation.

You should change it around into 96 add four, subtract seven.

Lucas says, "Start with 96 add four, because it equals 100." So 96 add four equals 100, and then subtract seven.

Lucas says, "10 subtract seven equals three.

100 subtract seven equals 93." So very well done if you reordered that calculation and you managed to get the right answer.

Izzy and Lucas sort these problems. So there's four problems they're going to sort.

Should we reorder the steps or keep them in the same order? Let's look at that first problem, so 49 subtract nine, add three.

Lucas says, "47 add three equals 50.

It would be more efficient to order the steps." So more efficient to reorder the steps in that calculation to start with 47 add three.

Let's look at the next calculation.

So 105 add 17, subtract 5, would you keep the same order or would you reorder the steps? "105 subtract five equals 100," says Izzy.

It would be more efficient to reorder the steps.

So we have to change that around and do 105 subtract five and then add the 17.

So that one also we need to reorder the steps.

Look at the next calculation.

So the next calculation is 84 add six, subtract seven.

How would you calculate that one? Lucas says, "84 add six equals 90.

It will be easier to keep the same order." Let's look at that last calculation.

So 145 subtract 15, add nine, would you keep the same order? Would you reorder the steps? Izzy says, "145 subtract 15 equals 130.

130 add nine equals 139.

It would be easier to keep the same order." Because of the numbers involved, it's quite easy to calculate that one in the order it already is.

So Izzy says, "Let's put that one in keep the same order." Sort these problems, so we've got two problems to solve there.

119 add eight, subtract nine and 225 subtract 25, add 19.

Would you keep the same order or would you reorder the steps? Now, pause the video and have a go at those two problems. Think about how you would organise them onto that table.

And welcome back.

Let's see how you sorted them.

Let's see if you agree with Izzy.

So for the first one, Izzy says, "119 subtract nine equals 110, 110 add eight equals 118.

It would be easier to reorder the steps." So Lucas says, "225 subtract 25 equals 200 and then 200 add 19 equals 219.

It would be easier to keep the same order." So Lucas doesn't think we should reorder that one.

So hopefully you sorted those two problems into the same places that Izzy and Lucas did, and remember, it's all about looking at the numbers involved.

And here is task A.

So in task A, you're going to be sorting the problems. Think carefully about whether you need to reorder the steps.

So do you keep the same order or do you reorder the steps? And what would be the most efficient way of working out the answer.

And if you get time as well, and you might want to do this as you go along as you're sorting them, can you also work out the answers to the problems as well? So here are the 12 calculations that you are going to be sorting, and think about the most efficient way to find the answer.

Pause the video and have a go at task A.

And welcome back, let's have a look to see how you got on.

So here are the answers.

This is how Lucas and Izzy sorted them and if you were looking really carefully at the numbers, you probably sorted them in the same way.

So that first one on keep the same order, we've got 48 add two, subtract nine.

48 add two equals 50, we add to a multiple of 10 and then we can easily subtract nine.

For reorder the steps, we've got 56 add nine subtract six.

Well, it's easier to subtract the six first of all.

56 subtract six equals 50 and then add the nine to get the answer of 59.

Very well done if you organised those in the same way that Lucas and Izzy did and very, very well done indeed if you managed to answer some of the questions as well.

Absolutely brilliant work.

And let's move on to part two of the lesson.

Part two of the lesson is, calculating with addends and subtrahends.

Let's take a look at the first problem.

So there are 213 people on a train.

At the next stop, 35 people get on and 34 people leave the train.

How many people are on the train now? "What calculation would give you the answer to the problem?" asks Izzy.

So it's 213 add 35, subtract 34.

"That looks like a difficult problem to solve," says Lucas.

I agree, Lucas, there's quite a lot of calculating involved in that, isn't there? So how should you solve the problem? For the addend, remember is the amount added and the subtrahend is the amount subtracted.

"We could reorder the calculation," says Izzy.

Sounds like a sensible idea.

So we could reorder into 213 subtract 34, add 35.

Lucas says, "I'm not sure that makes it any easier, Izzy." So the calculation is still just as difficult as it was before Izzy reordered it.

Maybe there's a different way of solving the problem.

Izzy focuses on the addend and the subtrahend.

So remember, we add 35 and we subtract 34.

Let's focus on that part.

"I know," says Izzy, "35 people get on the train and 34 people leave it.

That means that one more person gets on than leaves." So 35 people get on and 34 people get off the train.

That's the same really as one person getting on.

35 subtract 34 equals one.

"So how many people are on the train?" ask Lucas.

213 add one equals 214.

"There are 214 people on the train," says Izzy.

So 213 add one equals 214.

Izzy and Lucas look at some other problems. So we've got there, a bit of an easier calculation this one.

So 17 add six, subtract five.

Here's 17 and 6 represented as tens frames.

Let's look at the addend and the subtrahend first.

So we've got to start with 17 and we're adding six and subtracting five.

And Izzy's saying, "Let's focus on the add six, subtract five part of the calculation first." We've got to add six, then subtract five.

We could subtract five from the six.

So here's six represented in the tens frame and we're going to subtract five from that six.

"Six subtract five equals one," says Lucas.

Exactly, and then 17 add one equals 18.

So rather than adding six then subtracting five, Izzy's saying, "Just add one." 17 add one equals 18.

So 17 add 6 subtract five, the answer is 18.

Izzy and Lucas look at another problem together.

Quite a tricky problem this one.

So 74 add 60, subtract 50.

"Let's represent the problem using base ten blocks," says Izzy.

So here's 74 and we're adding 60 to it.

Let's again focus on the addend and the subtrahend.

So we're adding 60 and then subtracting 50.

"We've got to add 60 then subtract 50," says Lucas.

We can calculate 60 subtract 50 first.

And Lucas says, "60 subtract 50 equals 10." So let's use the base ten blocks to help us, so 60 subtract 50 equals 10.

74 add 10 equals 84.

So 74 add 60, subtract 50, the answer is 84.

But it's much more efficient, it's much easier to look at the addend and subtrahend first of all.

There are 351 people a train.

At the next stop, 53 people get on and 43 people leave the train.

How many people are on the train now? "So what calculation would give the answer to the problem," says Izzy.

The calculation would be 351 add 53, subtract 43.

"I think we should look at the addend and subtrahend first," says Lucas.

Lucas thinks he can solve the problem.

I can calculate 53 subtract 43 first.

So Lucas is going to focus on that addend and the subtrahend first of all.

We're adding 53 and then subtracting 43.

53 subtract 43 equals 10 and then I have to add 10 to 351.

351 add 10 equals 361.

So the answer is 361.

351 add 53, subtract 43 equals 361.

Solve this problem as efficiently as you can.

So the calculation is 86 add 30, subtract 29.

How would you solve this problem? Pause the video, see if you can find the answer.

And welcome back, let's have a look to see how you got on.

So it's 86 add 30, subtract 29.

Of 30 and 29, there's only one difference between those two numbers, isn't there? So let's focus on the addend and the subtrahend first of all.

We're adding 30 and then subtracting 29.

So calculate 30 subtract 29 first.

So 30 subtract 29 equals one.

Then add one to 86.

86 add one equals 87.

86 add one will give the same answer as 86 add 30, subtract 29, so the answer is 87.

Very well done if you thought really carefully about how to answer that question.

Izzy and Lucas look at another problem together.

So this time they got the calculation, 287 subtract 48, add 50.

They're going to focus on the addend and the subtrahend first of all.

There's a slight difference this time, isn't there? We're subtracting first of all and then adding.

Now Izzy is saying, "It doesn't matter that the subtraction part comes first.

We can still calculate 50 subtract 48 first of all." So when we're adding and subtracting a number, it doesn't matter what order they come on, we can reorder it and it will still give the same answer.

So we could first of all work out 50 subtract 48.

50 subtract 48 equals two.

And then we add two to 287.

287 add two equals 289.

So the answer is 289.

Solve this problem as efficiently as you can.

So the calculation this time is 116 subtract 30, add 40.

How would you solve that problem? Pause the video and see if you can find the answer.

And welcome back.

Did you manage to find the answer? Did you think carefully about the most efficient way to solve the problem? So let's focus on the subtrahend and the addend first of all, because we're subtracting 30 and adding 40, and it's quite easy to work out the difference between 30 and 40.

Izzy says, "Calculate 40 subtract 30 first of all." 40 subtract 30 equals 10.

And Lucas says, "Then add 10 to 116." 116 add 10 equals 126.

So the answer is 126.

So well done if you got that as an answer and excellent work if you looked really carefully at the subtrahend and the addend and you reordered the two numbers and subtracted 30 from 40 to get 10.

Very, very well done indeed.

And let's have a look at task B.

So the first part of task B, you got to calculate each answer efficiently.

Now, you may need to reorder some calculations as well, so look really, really carefully at those calculations.

How are you going to work out the answer? And if you need to reorder them, you can do any jottings, any writing down of equations underneath, that will be absolutely brilliant to help you work out the answer.

And here's part two of task B.

So read each question carefully and write the calculation.

Calculate each answer efficiently.

So A says, "There are 337 people on a train.

At the next stop, 46 people get on and 45 people leave the train.

How many people are on the train now?" So think really, really carefully about the calculation you'd have to do.

Do you need to reorder the calculation at all to work out the answer? And then part three, calculate each answer efficiently.

Use what you've learned from the whole lesson today.

Should you reorder the steps or keep them in the same order? So there's all sorts of different problems there.

How would you work out the answer? So pause the video and have a go at task B.

Welcome back, and let's take a look at how you got on.

So here are the answers for part one of task B.

Here are the answers for part two of task B.

So for that first problem, the calculation you should've written down is 377 add 46, subtract 45, and the answer is 378.

If we're adding 46 and subtracting 45, that is the same as adding one and 377 add one equals 378.

And here are the answers for part three of task B.

So very well done if you got on to part three and hopefully you've used everything you've learned in today's lesson to help you work out the answers.

Now, question A was 627 add three, subtract 30 and the most efficient way of calculating the answer there was to add three to 627, that gives you the answer 630 and then subtract 30, that gives you the answer 600.

And then for F, the question was 787 subtract 89, add 90.

Well, if we're subtracting 89 and adding 90, that's the same as adding 90 and then subtracting 89, which is the same as adding one.

So 787 add one equals 788.

Very well done for completing task B and hopefully you're feeling much more confident today with calculating multi-step problems and thinking carefully about the most efficient way of finding the answer.

And here is our lesson summary.

So look for efficient ways to calculate answers.

Reorder calculations.

Think about whether to add or subtract first.

Look for calculations that result in multiples of 10 or 100.

And sometimes you should subtract the subtrahend from the addend first.