Lesson video

Hello there.

My name is Mr. Goldie and welcome to today's maths lesson.

And here is our lesson outcome.

I can understand why the order of addition and subtraction steps can be chosen.

And here are our keywords.

In fact, there's only one keyword today and that keyword is reorder.

Can you say that? Reorder.

Reorder means arrange something in a different way.

And here is our lesson outline.

So in the first part of the lesson, you're going to be reordering addition and subtraction steps, and in the second part of the lesson you're going to be rewriting and matching multi-step problems. Let's get started.

In this lesson you will meet Lucas and Izzy and they're going to be doing lots of maths with you today.

Let's look at our first problem.

There are 12 people on a bus.

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

There's our three people getting on the bus and there's our five people getting off the bus.

How many people are on the bus now? What calculation would you do to work out the answer? So we have 12 people on the bus, three people got on the bus and five people got off.

So the calculation would be 12, add three, subtract five.

Let's look at another problem.

There are 12 people on the bus.

Here are 12 people on the bus.

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

So five people get off the bus and three people get on.

How many people are on the bus now? Asks Izzy.

Lucas says, what calculation would you do to work out the answer? So there are 12 people on the bus, five people get off the bus, three people get on.

So the calculation would be 12, subtract five, add three.

Is 12, subtract five, add three equal to 12, add three, subtract five? What do you think? Izzy says, I don't think they can be equal because the numbers are added and subtracted in different orders.

We've got 12, subtract five, add three and 12, add three, subtract five.

Luca says, I'm not sure, they could be equal.

Let's find out.

Good idea, Lucas.

Izzy and Lucas represent both problems using tens frames.

So let's have a go at trying to do 12, add three, subtract five.

Izzy says I'm going to start with 12 and add three.

There's 12, represented in the tens frames and Izzy adds three.

Now I'm going to subtract five, says Izzy.

So Izzy now subtracts five.

What's left? 10, 12, add three, subtract five equals 10.

Lucas says I'm going to start with 12 and subtract five.

So there's 12 represented in the tens frames.

Lucas subtracts five.

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

Lucas then adds the three.

The answer is 10.

What do you notice? Have you spotted something? You probably spotted that the answer to both problems is 10.

So does it matter what order the steps are in? We're going to compare the calculations using number lines.

I don't think Izzy's convinced yet that they are completely the same.

So Izzy's going to have a go at calculating 12, add three, subtract five.

There's a number line.

Izzy starts from 12 and adds three, gets to 15, then she subtracts five and gets to 10.

The answer is 10.

Now let's have a look at 12, subtract five, add three.

So start from 12.

We subtract five, first of all, that counts back to seven and then we add three to seven and that gives the answer 10.

So 12, subtract five, add three is also 10.

Both calculations give the same answer, says Lucas.

If the steps are the same, the order does not matter.

So we've started with 12 and we added three and subtracted five, but it doesn't matter which order you add the three and subtract the five, it still gives the same answer.

Let's have a look at this problem here.

So what is 18, add two, subtract seven? I'm going to start with 18 and add two, says Izzy.

There's 18 represented in tens frames.

Izzy adds two, that gives the answer 20.

And now, she says, I'm going to subtract seven.

So Izzy subtracts seven and that gives the number 13.

So 18, add two, subtract seven equals 13.

What is 18, subtract seven, add two.

Have a go at that problem.

What do you get as the answer? You could use tens frames to help you work out the answer or draw a number line or count something out to help you.

Whichever method you would like to use.

But can you try to work out the answer to 18, subtract seven, add two? Pause the video and have a go at that problem.

And welcome back.

How did you get on? Did you manage to get an answer? Did you get the same answer that Izzy got? Let's have a look.

So Lucas says I'm going to start with 18 and subtract seven.

So here's 18 represented in our tens frames, and Lucas subtracts seven.

That counts back to the number 11.

So we're left with 11.

Now I'm going to add two, says Lucas.

So Lucas adds two to get the answer.

So 18, subtract seven, add two, equals 13.

So it doesn't matter what order the steps are in, as long as the steps are the same size, they can be in different orders and you'll still get the same answer.

The answer to 18, add two, subtract seven is the same as the answer to 18 subtract seven, add two.

Is 13, add two, subtract six equal to 13, subtract six, add two? We're going to compare the calculations using number lines, says Izzy.

So 13, add two, subtract six.

Let's have a go trying to work out the answer to that one first of all.

There's the number line.

Starts on 13.

We're going to add two, that counts up to 15.

And then subtract six.

15, subtract six, equals nine.

So the answer to that calculation is nine.

13, add two, subtract six, equals nine.

Let's have a go with 13, subtract six, add two.

So this time we're gonna start with 13, we're going to count back six, we're going to subtract six, 13, subtract six equals seven and then we're going to add two.

Seven, add two, equals nine.

It's the same answer.

Both calculations give the same answer.

If the steps are the same size, the order does not matter.

If we start from 13 and we're adding two and subtracting six, it doesn't matter what order those two steps come in, we can add the two first and then subtract the six or subtract the six and then add the two.

Still gives the same answer.

If the steps are the same size, the order does not matter.

Here's calculation 13, add two, subtract six.

We're going to reorder the steps in 13, add two, subtract six.

Let's start by breaking the equation up into different steps, says Lucas.

So we've got there 13, add two, subtract six, equals nine.

Let's reorder the steps.

So we're still starting with 13.

13 is the last starting number.

We're going to subtract six first and then we're going to add two.

And the answer is still nine.

All we've done is reorder those steps.

The steps have not changed, they just happen in a different order.

Is 15, add three, subtract four, equal to 15, subtract three, add four? What do you think? So we're going to compare the calculations using number lines, says Izzy.

Let's have a go, first of all at 15, add three, subtract four.

Start from 15.

We're going to add three.

(indistinct) the answer 18, and then we're going to subtract four, 18, subtract four, equals 14.

So the answer to that calculation is 14.

What about 15, subtract three, add four? So again, we're going to start from 15.

Going to subtract three.

I guess that's the answer, 12, and then we're going to add four.

I get the answer 16.

The answers are not the same.

Why are the answers not the same? Izzy and Lucas compare the calculations.

I'm going to break up the calculation to different steps, says Izzy.

So Izzy breaks up the calculation to 15, add three, subtract four, so it's nice and clear, those different steps that Izzy's doing.

I will do the same for my calculations, says Lucas.

So 15, subtract three, add four.

15, subtract three, add four.

Let's reorder the steps.

We're not going to reorder the steps in Izzy's calculation.

We're going to reorder the steps in Lucas's calculation so we can compare the two calculations and see if they're the same.

So let's start with 15 and add four first of all and then subtract three.

What do you notice? The steps in the two calculations are not the same.

Different numbers are added and subtracted.

So Izzy starts with 15, she adds three, then subtracts four.

Lucas starts with 15, he adds four and subtracts three.

So 15, add three, subtract four is not equal to 15, subtract three, add four.

The steps involved are different in those two calculations.

True or false? 11, add two, subtract three is equal to 11, subtract three, add two? It's true.

In both calculations, two is added and three is subtracted.

So we go breaking that up into the different steps.

We've got 11, add two, subtract three.

We can rearrange that into 11, subtract three, add two.

They're both equal.

Here's one to try on your own.

True or false? 10, add four, subtract five is equal to 10, subtract five, add four.

Pause the video and see if you can work out to see whether that is true or false.

And welcome back.

What do you think? Is it true or false? Let's have a look.

It is true.

In both calculations, four is added and five is subtracted.

So here we've got 10, add four, subtract five and we can rearrange that into 10, subtract five, add four.

The steps are still the same, they've just been rearranged.

Well done if you said that was true.

And let's take a look at task A.

So in task A, you have to work out whether these are true or false and you've got to circle the correct answer.

So one, A, says, nine, add two, subtract five is equal to nine, subtract five, add two.

Is that true or is that false? Look at those steps carefully.

Are they equal? And if you're really, really stuck, you can always try and work out the answer to both and see whether the answers are the same.

So there's part one of task A, and here's part two of task A.

Circle the calculation, which would give you the same answer.

Let's have a look at two A, first of all.

So which calculation is equal to six, subtract two, add five? Is it six, add two, subtract two? Is it six, subtract five, add two? Is it six, add five, subtract two? So there's task A.

Pause the video and have a go at task A.

And welcome back.

Let's take a look at those answers and see whether you got them right.

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

So nine, add two, subtract five is equal to nine, subtract five, add two.

That is true.

So very well done, if you said that was true.

And have a look at those other answers there.

Check it against your work, see whether you got them right.

Let's look at part two of task A.

So you had to circle a calculation which gives the same answer.

So for that first one, for A, six, subtract two, add five is the same as or would give you the same answer as six, add five, subtract two.

And again, look carefully at your answers.

Did you give the same answers as the ones there? Very well done if you did.

And let's move on to the second part of the lesson, which is matching and rewriting multi-step problems. Izzy and Lucas are matching problems with the same answer.

We're matching problems where the same numbers are added and subtracted, says Izzy.

Matching problems also start with the same number, says Lucas.

So 12, subtract two, add four, 17, add four, subtract two and 12, subtract four, add two.

You've got to match them up to those calculations opposite.

So 17, subtract two, add four, 12, add four, subtract two and 12, add two, subtract four, which ones match together? Let's take a look.

So 12, subtract two, add four, we give the same answer as 12, add four, subtract two.

The steps are the same in both calculations.

All that's happened is they've been reordered slightly.

So they both start with 12.

Four is added and two is subtracted.

Let's look at a different one.

So 17, add four, subtract two is the same as 17, subtract two, add four.

They both start with 17.

Four is added and two is subtracted.

That means those last two match up as well.

So they both start with 12.

Four is subtracted in both those calculations and two is added.

So they would both give the same answer.

Match problems that are equal.

So match problems where the same numbers are added and subtracted.

Problems that match also start with the same number.

So here are three calculations.

Can you match each of them up with one of those calculations over this side? So pause the video and have a go trying to match up those calculations.

And welcome back.

Did you manage to match them up correctly? Let's take a look, see whether you did it right.

Those two calculations there match together.

They both start with 15, one is subtracted and five is added.

So well done if you spotted those two.

These two here also match.

They both start with 15, one is added and five is subtracted.

So well done if you matched those two.

And finally, these two here match.

So they both start with 13, one is subtracted and five is added.

So very well done if you matched those up correctly.

Let's look at our next problem.

So is 13, subtract two, add four equal to 13, add five, subtract three? I don't think they can be equal because different numbers are added and subtracted.

They both start with the same number, 13, but Izzy is saying in one of them, five is added and the other one, four is added.

And in one of them, two is subtracted, and in the other calculation, three is subtracted.

Let's take a look whether they are equal or not.

Let's start with 13, subtract two, add four.

Let's represent it using tens frames.

Let's start with 13.

We're going to subtract two and add four.

So 13, subtract two, add four equals 15.

Let's have a go at the other calculation.

So 13, add five, subtract three.

Let's represent it again using tens frames.

Let's start with 13.

We're going to add five this time.

So we add five on and then subtract three.

The answer's also 15.

Hang on, they are equal.

Different numbers are added and subtracted, but both answers are the same.

So problems can have equal answers even when different numbers are added and subtracted.

So be careful.

Just because there are different numbers involved doesn't mean that the answers won't be equal to each other.

Izzy and Lucas reorder calculations by changing the order as steps.

I'm going to reorder 16, subtract five, add four, says Izzy.

So she's broken it up into the steps.

So 16, subtract five, add four, and she's going to reorder it, so it becomes 16, add four, subtract five.

So the answer to both of those would be equal.

16, subtract five, add four is equal to 16, add four, subtract five.

Well done, Izzy.

I'm going to reorder 12, add five, subtract two, says Lucas.

So here's 12, add five, subtract two, broken down to those steps, and Lucas reorders that calculation.

So 12, subtract two, add five.

So 12, add five, subtract two is equal to 12, subtract two, add five.

Well done, Lucas.

Lucas rewrites 15, add six, subtract five.

He reorders the steps in the problem.

So here's 15, add six, subtract five, and Lucas is going to rewrite, reorder the steps in the problem.

So we still start with 15, we're going to subtract five, first of all, and then add the six.

15, add six, subtract five is equal to 15, subtract five, add six.

Rewrite 14, subtract three, add five.

Reorder the steps in the problem.

So pause the video and have a go at trying to reorder the steps in the calculation, 14, subtract three, add five.

And welcome back.

Let's see how you got on.

Let's see whether you got it right.

So you might have broken the problem up into the different steps.

So 14, subtract three, add five, and then you might have used that to help you reorder the steps.

So 14, add five, subtract three.

And 14, subtract three, add five is equal to 14, add five, subtract three.

Well done if you managed to reorder that calculation correctly.

Izzy and Lucas are calculating 13, subtract four, add five.

They reorder the steps in the calculation.

I'm going to calculate 13, add five, subtract four, says Izzy.

I'm going to calculate 13, add four, subtract five, says Lucas.

Who has reordered the steps correctly? What do you think? Who do you think has reordered the steps correctly? Who do you think has made a mistake? Izzy is correct.

13, subtract four, add five equals 13, add five, subtract four.

Lucas is incorrect.

13, subtract four, add five does not equal 13, add four, subtract five.

Sorry, Lucas.

Reorder the calculation, 11, subtract six, add three.

Change the order of the steps.

So pause the video and see if you can work out what 11, subtract six, add three would be if you've reordered the steps.

Pause the video and have a go reordering the calculation.

And welcome back.

Now, you should have written 11, add three, subtract six.

Very well done if that's what you wrote.

And let's move on to task B.

In part one of task B, you have to match the problems that give the same answer.

So you've got some problems to cut up and sort and you've got to match them to the correct problem that will give the same answer.

So we've got there, the first one is 10, add four, subtract three.

You've got to look to see which one of these will give the same answer.

So you're looking to see one where the steps have been reordered and that will give the same answer.

That's your first task, matching the calculations.

Part two of task B, you've got to rewrite each problem by reordering the steps.

So nine, add to subtract four is equal to nine, and what are the steps in the other order? So pause the video and have a go at task B.

And welcome back.

How did you get on? Quite a lot to do there, wasn't there? Let's have a look at the answers and see how you got on.

Here are the answers for part one of task B.

So 10, add four, subtract three matches the calculation, 10, subtract three, add four.

They will both give the same answer.

And seven, add three, subtract two, but give the same answer as seven, subtract two, add three.

Very well done if you managed to match those up correctly.

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

So nine, add two, subtract four is equal to nine, subtract four, add two.

12, subtract one, add three is equal to 12, add three, subtract one.

So very well done if you managed to reorder the steps in those calculations.

Excellent work in your maths today and hopefully you're feeling much more confident at understanding why the steps in addition and subtraction problems can be chosen.

And let's move on to our lesson summary.

So if the steps are the same size, the order does not matter.

As long as you start on the same number, you will get the same answer.

Problems can have equal answers even when different numbers are added and subtracted.