Lesson video

Hello.

My name is Mrs. Knight, and I'm here to teach you your Maths lesson today.

You'll need your practise activity from the last lesson, a pen or pencil and some paper.

Press pause, go and find what you need, and then we can begin the lesson.

Hello again, here's the practise question Mrs. Grimes left you with.

How did you choose to represent your answer? Did you use a number line? Or a bar model or jottings? And how did you use the stem sentence to help you? This is how I chose to do it.

First, I chose to represent my solution on the number line.

Mollie's total distance from school, minuend, was 1400 metres.

The distance she walked is the subtrahend, which is 850 metres.

When I subtract 850 from 1400, the difference is 550.

Then she then walked a further 100 metres.

I know that if the minuend stays the same, what I add to the subtrahend, I subtract the same amount from the difference, because that's what we learnt with Mrs. Grimes in the last lesson.

She's walked a further 100 metres, so my subtrahend increases by 100 to 950.

This means that the difference must decrease by 100, is this what you got? Let's try putting that into our stem sentence.

I've kept the minuend the same and added 100 to the subtrahend, so I must subtract 100 from the difference.

So if you choose to represent it using a bar model, I've tried it that way as well, and here's how I did it.

Minuend is the total journey from school to home, 1400.

So that's in my top bar.

She walked 850 metres which gave us a difference of 550 metres.

But when she walked on an additional 100 metres, the blue bar in my model representing a subtrahend, needs increased by a 100, to become 950 metres.

This means that the bar representing the difference needs to decrease by the same amount, which gives us a difference of 450 metres.

Some of you might have chosen jottings to represent the problem.

This is what my jottings look like.

I like this way of solving the problem, because it's really clear for me to see how the increase in the subtrahend must be balanced by a decrease in the difference.

So if I add 100 from the subtrahend, I need to subtract 100 here, which gives me an overall distance difference of 450.

SO in this lesson, we're now going to look at when the subtrahend decreases.

Mollie's home is also a 1400 metre walk to her friend's Ellie's house.

She walked 575 metres.

How much further does she need to walk? Well, the total distance from her home to Ellie's house is still 1400 metres.

So this is still our minuend.

And the distance she walked is the subtrahend, 575 metres.

So by subtracting the subtrahend from the minuend, we can see how much further that she has to go, the difference, 825 metres.

Now what would happen if Mollie got part of the way to her friend's house and realised she'd dropped her coat? Well, she'd need to go back and pick it up, wouldn't she? So she don't get into trouble when she got home.

Let's have a think about how we could solve this.

What happens when she turns around and goes back on herself, will she be getting close to her home, or to her friend's house? Have a think.

That's right, she'll be getting close to home, and further away from where she wants to get to, because she starts by travelling towards her friend's house.

But when she turns round, she goes back on herself.

Let's have a think about how we could represent this.

The total distance is 1400 metres, she's walked 575, so she needs to walk a further 825 to get to Ellie's house.

If she walks back to her home, to look for her coat, the distance represented by the subtrahend will decrease.

The subtrahend would be 575 subtract 150.

The subtrahend has decreased by 150.

And the difference? That's right, it's increased by 150.

I can show you this with jottings too.

Here's the equation representing the first part of Mollie's journey.

And then when she forgot her coat and had to go back, here are the jottings representing the second part of her journey.

Now have a careful look at them, what's the same about them? And what's different between these, and the jottings we use for the previous question.

Have a think, pause the video if you need to.

And look back at what we did before.

Here's our question for today.

Raf has saved some money, He wants to buy a games console the cost more money he has saved.

How much more does he need to save? How much more does he need to save? That's an odd question when we don't know how what the games console costs or how money money he has.

What could I draw to represent this problem? Pause this lesson now, while you have a think about how you could do this, and jot your ideas on a piece of paper.

Hello again.

Have you thought about how you could represent the problem? Let's think of how we'd organise the information, if we did have it.

I know the cost of the games console is going to be my minuend.

And from that, I can subtract how much he saved, and that will tell me how much more he needs to save.

And I think we can put the mathematical vocabulary we've learned, insert equation to explain what each part of it is there for.

The cost of the games Consoles is the minuend, his savings are the subtrahend, and so how much more he needs to save, is the difference.

Now we can work this out.

Let's look at the problem with numbers in, so we can work out how much he needs to save.

Raf has saved 150 pounds.

He wants to buy a games console that costs 350.

How much does he need to save? 350 subtract 150 is equal to 200.

That's too easy, he's a bit like my brother used to be.

He can't wait till he's saved enough money before he starts spending.

My granddad used to say that money was burning a hole in his pocket.

So Raf's gone online and he spend 20 pounds of his savings, so now he's got 130 pounds.

How much money does he need to save now, before he'll buy the games console? Let's have a think.

Have his savings increased, or have they decreased? That's right, if he spent some of his savings, the amount he has will have decreased, so now he needs to save more.

And we write an equation to help us find out how much he needs to save.

What's the same as the last question? What's different? Well, we know that the games console hasn't changed its price, what has changed is the amount of money that he's got.

So the minuend will stay the same, but the subtrahend that represents his savings has decreased.

Now I could calculate this, but I feel there's an easier way of doing it.

What have we already learnt that we could use? Have a think about the last two lessons.

What happens in an equation when the minuend stays the same but the the subtrahends changes? That's right.

We need to change the difference by the same amount.

That means, we could use our stem sentence.

Lets say it together.

I've kept the minuend the same, and I subtracted mmh from the subtrahend so I must add mmh to the difference.

Now, could we put the numbers from this equation into a stem sentence.

What's our subtrahend has changed by? It's changed by the 20 pounds, hasn't it? The 20 pounds that Raf has spent, so we can say, I kept the minuend the same, I've subtracted 20 from the subtrahend, so I must add 20 to the difference.

Let's think about how we represented the problem when Mollie was travelling home from school.

We were able to show the change in her journey on a number line, that I want to show Raf's problem on a number line too.

So here is our number line, with the first equation.

350 subtract 150.

And here is the second equation.

350 subtract 130, because his savings have now decreased by 20.

That's the difference in the subtrahend.

So if I have subtracted 20 from the subtrahend, I need to add the same amount to the difference.

Let's try that with our stem sentence again.

I've kept the minuend the same and I've subtracted 20 from the subtrahend, so I must add 20 to the difference.

We could look at that on a bar model as well.

We can see that I've got a white bar, representing the subtrahend, his savings of 150 pounds.

Then his savings decrease by 20.

So the blue bar representing the amount he has left to save, must increase by 20.

And just like before, I could choose to represent this as jottings as well like this.

Subtraction from the subtrahend, adding the same amount to the difference.

Now two lessons ago, we learned that the more we're subtract, the less we are left with.

Or the less we subtract, the more we're left with.

In Mrs. Grimes lesson, We had a new generalisation that said, if the minuend is kept the same and the subtrahend increases, the difference decreases by the same amount.

So today I think we can add another generalisation.

If the minuend is kept the same and the subtrahend decreases, the difference increases by the same amount.

You might want to jot that generalisation down, because it's time for you to work on your own now.

And using the generalisation will really help you to work out the answers, without having to calculate everything from the beginning each time.

So if you need to pause the video now so you can jot this down, do that now.

Now it's your turn.

This is what I'd like you to do before the next lesson.

Don't forget to identify the minuend, subtrahend, and difference in each part of the question before you start, like we did together.

Think as well about how you're going to represent the equation.

Which of the models we've used today will you use? Will it be a number line, a bar model or jottings, or another way that I haven't thought of.

If you need to, you're welcome to watch all or parts of this lesson again, to remind yourself what the generalisation is.

Good luck, have fun, and we'll see you in the next lesson.