Lesson video

Hi, my name is Mr. Coombs, and I'm going to be guiding you through your math lesson today.

Just like in previous lessons, you'll need a pen or a pencil and a piece of paper to be able to jot a few things down.

If you pause the video, go and get those things now, and then when you return, we'll begin.

Welcome back.

Did you manage to find everything? Okay? Brilliant.

Let's begin.

Think back to the end of the last lesson.

We set you this challenge and we asked you to remember the STEM sentence in generalisation that we were able to make.

Can you remember what that was? Should we read it together? If the minuend and subtrahend are changed by the same amount, the difference stays the same.

And that is key for today's learning.

We're going to fly through a few examples and end up looking at the difference between five, between two, five digit numbers.

Let's look at our first calculation and then look at the second calculation and see how the minuend and subtrahend have changed.

Have you spotted it? Yeah, they're both decreased by two.

I've subtracted two by both.

And because I've done the same to the minuend and the subtrahend, it means my difference is still the same.

So it means my difference is still six.

Well done.

There's two ways you could look at the next question.

We could look at the previous calculation, of 98 subtract 92, or we could go back to the original calculation.

And again we're seeing what's happened to our minuend and subtrahend.

So from the original one, I've subtracted four and subtracted four.

From the previous calculation, you'll see I've subtracted two and I've still subtracted two.

Either way, I've done the same to the minuend and the subtrahend which means my difference stays the same.

So it's six.

Now the next one is asking you in a slightly different way but if we understand that generalisation we're able to use that understanding to solve it.

So it's now asking us to find a missing subtrahend.

The minuend is 94.

The difference is still six.

So let's look at what's happened from the original minuend of 100.

That's right.

I've decreased by six.

I've subtracted six.

So what does that mean I need to do in order to keep the difference the same? Well done.

Subtract six from the subtrahend.

So now I've got 94.

I need to subtract that six to keep the difference the same.

It will give me the answer 88.

Excellent.

Well done.

Everyone happy with that? Well then, it's exactly the same for the next one.

We could go and look at these calculations helpers.

Or we could go back to the original to be able to fill it in.

Either way, we will understand that they missing subtrahend is 86.

And again, these final two calculations, they're asking us to find it in a slightly different way.

They're asking us to find the missing minuend.

So again, I understand that the subtrahend is given, and that the difference is given.

The difference is still six.

So if I see what's happened to my subtrahend comparing it to either the calculation above or going back to that original calculation, I'm able to find out what that missing minuend is.

You find it easy, I know.

It's so simple when you understand what's happening.

Well done.

Let's fill every last to it.

* And let's move on to the challenge question from yesterday.

The first one was 90 and then the last one.

Brilliant.

Is 88.

Great work, everyone.

Here's the challenge question that we were set at the end of the last session.

And it was about Felicity and the amount of marbles that she has.

We were told that she has 23 more red marbles than she does blue marbles.

And then something changes.

Something changes to the blue marbles and the red marbles because she gave 12 away.

So they decreased by 12.

It was about the difference.

The difference to start with was 23.

And then she subtracted 12 from both the red marbles and the blue marbles.

There is a decrease of the same for both the minuend and the subtrahend.

What does this mean? Brilliant.

It means the difference has stayed the same.

A number line is a really clear way of showing this.

We've got our blue and we've got our red marbles and we knew at the start that the difference was 23.

We then decreased that amount by 12.

And remember it was a decrease of 12 to both the blue marbles and the red marbles.

So this means that the difference is still 23 because you have done the same to both of the minuend and the subtrahend.

Therefore, the difference is still the same.

Another way of saying this would be that there are 23 more red marbles than blue marbles or you might even say there are 23 fewer blue marbles than red marbles.

Another really good way of representing that would be to look at a bar model.

So the bar model represents the red marbles.

Come on, join in.

The red marbles, we know, are more than the blue marbles.

So I'm going to have my blue box shorter than my red box.

And the blue box is obviously representing the blue marbles.

I know the difference.

So I can fill that in.

Always fill in the information that we know.

The difference is 23.

Then, she gave 12 away.

And so she's making her amounts smaller, less.

She's getting rid of her 12 marbles.

But just by doing the same to the red marbles and the blue marbles means that the difference stays the same.

Can you see that really clearly with that? She still has a difference of 23 marbles.

Let's look at those together.

You can see on the top, my bar models are longer in length because she had more marbles.

And in the second model, they're shorter because she's decreased them.

And we know she decreased them by 12, but because the red marbles decreased by 12 and the blue marbles decreased by 12, the difference stays the same.

So, in this lesson, we're going to use that generalisation from our last lesson and from those two activities to make our calculations easier to complete.

It's always nice to be able to find things easy.

So let's read that STEM sentence once more.

If the minuend and the subtrahend are changed by the same amount, the difference stays the same.

Look at the calculations that are given there.

Now I know most of you will be able to solve those straight away but it's not about solving those straight away.

It's about seeing the math and understanding what's happening.

Let's look to see how they are connected.

To start with, we have a minuend of 50 and a subtrahend of 25.

On the second calculation, that minuend changes to 49 and the subtrahend to 24.

What is that change? Well done.

They've decreased by one.

So that means the subtrahend had decreased by one.

And the minuend has decreased by one, which is the same amount.

So therefore the difference will be the same.

And as you look down, you'll see that that's what's happening each time.

So I now know that all of those calculations will have the same difference.

Let's use a number line.

Let's look at our first calculation.

You can see we've got 50 and 25 marked on our number line.

And we know that the difference is 25.

The next calculation asked us to find a difference between 49 and 24.

And you'll see that it moves along.

It subtracts one from the minuend and one from the subtrahend.

And the difference stayed the same.

what you get? The difference is staying the same each time because I'm doing the same to the minuend as I am to the subtrahend.

Now, what * More? Again the minuend has decreased by one.

The subtrahend as decreased by one.

So what do we expect our difference to be? The same.

It will still be 25.

I think that's a great way of seeing that generalisation that we made.

If the minuend and the subtrahend change by the same amount, the difference will stay the same.

Which one of these calculations did you find easier to complete? Try and tell somebody in your house.

And tell them why you found it easy to complete.

Pause the video and come back when you're ready.

Hi.

Welcome back.

Did you say that 50 subtract 25 was the easiest? I would imagine so.

And there's lots and lots of different reasons for that.

It might be the fact that it's just one of those non-facts because you've seen it so many times.

So it's automatically in your brain and you're able to recall that straight away.

It might be that you understand halves and you know that half of 50 is 25.

It might be the fact that you understand subtracting from multiples of 10 is really easy.

Whichever way, it's always good to find that easiest calculation first.

But could a calculation*, how would you think we could change, either the minuend or the subtrahend, to make that easier to calculate? Again, pause the video and think how you can transform that calculation to make it easier.

Can you change the minuend? Could you change the subtrahend? Is there only one way of doing it or is there more than one way of doing it? But which one did you think was the easiest? Welcome back Again, did you change the minuend? You could have subtracted three from the minuend to make it 50.

That would have been and easy calculation.

We've just done that, but I want you to look at seeing, can we change the subtrahend.

And, where possible, can we say change it to a multiple of 10? Because subtracting multiples of 10 are always easy.

So, what should we do? Do we need to decrease it or can we increase it? That's right.

If we increase that by one, we're on a multiple of 10.

We're on 40.

four tens.

So, because we've done that, we need to do the same to our minuend.

We need to increase it by one.

And that means we have a new calculation and I'm sure we're all confident to be able to answer that.

Remember, there's nothing wrong with writing that down in a written method, but if you can do it mentally, then brilliant.

So because we have changed the minuend and the subtrahend by the same amount, we know that the difference will stay the same.

So I can now confidently go back to my original calculation and answer that the difference between 53 and 39 is 14.

Look at this calculation and think, can we change the minuend or the subtrahend to be a multiple of 10? Yeah.

I think it's quite clear which one you change, but is it? because 79 is very close to being a multiple of 10, I just have to add one and I'm on 80.

But sometimes, it's not always easier to change the minuend.

When you're subtracting actually, if you can change the subtrahend to a multiple of 10, it's a lot easier to subtract a multiple of 10 rather than subtract from a multiple of 10.

Let's see what this would look like.

So the subtrahend is 46.

To change it to a multiple of 10, I would add four to get to 50.

And because I've added four to the subtrahend, I need to do the same to the minuend.

Add four.

So now I'm left with a calculation, 83 subtract 50 equals.

And that's quite a nice easy mental math calculation to complete.

Remember there's nothing wrong with writing it down if you need to, but we should be able to get the answer 33.

And because I followed that golden rule of changing the minuend and the subtrahend by the same amount, it means that the difference will stay the same.

So I can confidently answer 79 takeaway 76 is 33.

Look at the two calculations.

What's the same? What's different about them? Yeah, the difference is the same.

What's different is the minuend and the subtrahend.

And I certainly think one of those calculations is easier to complete.

Do you agree? You'll notice now that we've moved on to three digit numbers, but the important thing to remember is that the learning point is still the same.

If the minuend and the subtrahend are changed by the same amount, the difference stays the same.

Do you think you're going to be able to transform the minuend and the subtrahend to make this calculation easier to complete? Now that we're dealing with three digit numbers, it might be good to see can you make the number a multiple of 100.

And yes, you can see that quite easily, the subtrahend 205 could be changed to be 200 by subtracting five.

So, because I've done that, I need to make sure that I do the same to the minuend in order to keep the difference the same.

Subtract five gives me my new calculation, and taking away 200 from 861 is again a nice, simple mental calculation to give me my answer of 661 that I know is the same difference as the original calculation.

Again, look at those calculations.

Which one do you think is easier? Can you see just by changing the minuend or the subtrahend to be a multiple of 10 or a multiple of 100, can make our calculations easier to answer.

Now, let's look at this calculation.

I want to transform the calculations make it easier to solve.

I'd like you to pause the video.

And I want you to think about changing the minuend and the subtrahend to make this calculation easier.

Brilliant.

Have you got that written down? I wonder you he did the same as what I did first time.

I saw the 89 and thought that's easily changed to become a multiple of 10.

So I added one to get my 90.

I remembered my rule.

I had to add one to my minuend to make that 459.

And then I looked to that calculation and thought actually, that's not the easiest of calculations to complete.

It's still a little bit tricky.

I'm crashing that hundred boundary, And sometimes that does cause me a couple of issues.

So I want you to pause the video again and I want you to see if you could change that subtrahend to something else just to make it a really simple calculation.

Have a go.

Did you choose to make the subtrahend a multiple of 100? I know I did because 89 is 11 off being 100 and subtracting 100 from a number is a nice and simple calculation we can all do.

So, because I added 11 to the subtrahend, I needed to add 11 to the minuend.

Excellent.

Well done.

So now that calculation 469 subtract 100 is a nice easy mental calculation to complete to be able to find the difference.

And remember, because we did the same to the minuend that we did to the subtrahend, our differences stayed the same.

I'm confident now to say that the difference for the original calculation, 459 subtract 81 is 369.

So remember, sometimes we can change things in more than one way, but what we're always looking to do is find the easiest way because that mental calculation will make it a lot easier to calculate if for example, it was 100 rather than 90.

Another three digit by three digit calculation.

What's the difference between these two, three digit numbers? Well, we now know that we can change the minuend and the subtrahend to make this easier for us.

And we've actually discovered that change in subtrahend to a multiple of 10 or a multiple of 100 can make it really simple to answer.

So pause the video, have a go and see if you are able to find the easiest way to find a solution to this problem.

Well done.

Let's see if you've got the same.

I added 13 to my subtrahend to get 300 which means I have to do the same, to keep the difference the same, to the minuend.

I've added 13.

And look at that calculation now that we're having to complete, 369 subtract 300.

That's a nice, simple mental calculation fast to complete to have the difference.

And because we followed that rule I'm confident in answering the original question as having a difference of 69.

And that is all because we have got a solid understanding of that STEM sentence that we created.

Should we say it again? If the minuend and the subtrahend are changed by the same amount, the difference stays the same.

It doesn't matter what the numbers are, how large they are.

If we understand that, we're able to find a way to make things easier.

And we all like that.

Let's just test it and see if we can apply that understanding to larger numbers.

You'll see now I'm asking you to find the difference between two five digit numbers, but we just need to remember that generalisation.

I've left it on the screen for you.

If the minuend and the subtrahend are changed by the same amount, the difference stays the same.

How can we make this easier to answer? Could I change the subtrahend to be a multiple of 10 or a multiple of 1000 or possibly even a multiple of 1000 when dealing with five digit numbers? That's right.

203.

If I subtract three from 25,203, it's going to make that 25,200 and I need to do the same to the minuend.

So I subtract three to give me 45,225.

Why did we do this? We did it to make sure that the difference stays the same.

And because now we've done the same to the minuend that we've done to the subtrahend, we are confident that our differences stayed the same.

And that is an easier calculation to complete.

How do you think you might do that? Yeah, I did the same.

I did 225 subtract 200.

That gives me 25.

And then I subtracted the 45,000 subtract 25,000 to give me 20,000.

That gave me my answer 20,025.

And because I know that difference is the same as the original calculation, I'm confident in filling that answer in.

Wow.

You've worked really hard today.

I'm really impressed.

And do you know what? You should be impressed with yourselves as well.

Between now and your next lesson, I'm going to ask you to transform these calculations.

I'm going to see if you can apply that understanding of our STEM sentence to make these calculations easier to complete.

You'll see the first one, I set it out how we've been doing it.

This means that you can add the arrows to the minuend and the subtrahend to help you make sure you do the same to both.

That way, the different stays the same.

Remember, can you add or subtract that minuend and subtrahend to make this calculation easier? Multiples of 10.

Multiples of 100.

They really do make things easier.

I'm really impressed.

Your teacher, If for the next session, will go through the answers with you.

So make sure you bring your work with you.

Thank you for joining me.

I've really enjoyed it.

And remember, if you change the subtrahend and the minuend by the same amount, the difference will stay the same.

Goodbye.