Lesson video

Mrs. Knight here again, and I'm going to teach you your lesson again today.

You'll need the practise activity I sent you with at the end of the last lesson, a pen and pencil and some paper.

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

Here are the two questions I left you with at the end of the last lesson.

How did you choose to tackle them? Did you use a number line, or a bar model, or jottings, or another strategy of your own? Let's see how I went about solving the problems. As this problem is all about how far Beth and Kaisley had travelled, I decided to use a number line to solve it.

But before I could start to use my number line, I needed to identify the parts of the question.

The total distance, five kilometres, is the minuend.

But I remembered I get very confused when I mix up metres and kilometres in the same question, so I decided to change five kilometres into 5,000 metres, so I use the same unit of measure for the whole problem.

Then I identified the distance Beth has cycled, 1300 metres, is the subtrahend.

So I was able to put this information into an equation, that let me calculate the difference.

So first of all, I put Beth's journey onto my number line.

I then use this to work out how far Kaisley had cycled which then let me know how far he had left to go.

Because we knew that Kaisley had further to cycle than Beth, and that the subtrahend in the equation represents how far Beth had called, I need to subtract 240, the distance that Kaisley was behind Beth, from the subtrahend, to find out how far Kaisley had already cycled.

I was then able to put the new subtrahend into an equation for Kaisley, where you needed to balance the equation by adding 240 to the difference.

This told me how far he still had to go, 3,940.

And I knew that, because I used that same sentence from the last lesson.

So let's say it together just to remind ourselves what we did.

Are you ready? I've kept the minuend the same, but subtracted 240 from the subtrahend, so I must add 240 to the difference.

For this question, I chose to use jottings.

The number of points she needs, is the minuend, 25,000.

The number of points she scored already, 5,400, is the subtrahend.

The number of points she needs to win of the game, is the difference.

Here's the equation I used to work out that she needs 19,600 to win the game.

Now on the first part of the question, but the second part asked me how many points she needs to win after she loses 2000 points in a battle.

I remembered our generalisation; if the minuend is kept the same and subtrahend decreases, the difference increases by the same amount.

So I decreased my subtrahend by 2000 and then I increased the difference by 2000, and this let me work out how many more points Alex needed because I added 2000 to the difference, telling me that she now needed 21,600.

So here are the two generalisations from our last lessons; if the minuend is kept the same and the subtrahend increases, the different increases by the same amount.

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

We're can to carry on using them in our lesson today.

Let's have a look at this problem together.

Ciara has 85 marbles; 45 of them are red and the rest of the blue.

So she has 40 blue marbles.

Arjun also has 85 marbles.

Some of them are red and some of them are blue.

He has 10 more red marbles than Ciara.

How many blue marbles has Arjun have? Well, let's think.

What do we know and what do we need to find out? Well, we know how many marbles Ciara has and that 45 of them are red and 40 are blue.

And we can represent this in the equation like this, where the minuend is the total number of marbles and the subtrahend is the red marbles.

This tells us that the difference is the number of blue marbles.

We also know that Arjun has the same number of marbles as Ciara, 85.

But how could I work how many red and how many blue marbles he has? How could I represent it? We have Ciara's marbles represented on a part whole diagram.

We know that Arjun has 10 more red marbles than Ciara.

And we know from our last lesson, if we increase the subtrahend in an equation then we need to decrease the difference by the same amount so the equation still balances.

So, if the number of red marbles is increased by 10, the number of blue marbles must decreased by 10.

Here we can see they shown as jottings as well.

These show us that Arjun has 55 red marbles and 30 blue marbles.

Now it's your turn to have a go at a question like this by yourself.

Represent the problem using a part whole diagram and jottings like I did.

If you're fairly creative, how else could you represent the problem? Now, don't forget to use our generalisations to help you.

Pause the video now.

Welcome back.

How'd you get on? Did you use the generalisation 'cause I did? We know from our generalisation, that if the minuend is kept the same and the subtrahend decreases, the difference increases by the same amount.

Here's my solution.

Does yours look like this? In my equation, I increased the subtrahend by 18.

So I had to decrease the difference by 18 as well.

Did you decide that Arjun has 32 blue marbles? I'm sure you did.

Well done! Now, here's another way of thinking about this problem.

If we know how many red and blue marbles Ciara has, we could also write an addition equation to show the total, like this.

Now, do you remember when we had two addends, and if we increased one addend and decrease the other addend, by the same amount, the sum remains the same? Well, we could use that to write our solutions to problems like this.

This shows us, that Arjun had 32 blue mumbles.

Let's try another new problem.

Again, what do I know and what do I need to find out? Leah gets five pounds to spend on lunch each day.

So I know how much she has to spend and that's going to be my minuend.

I also know that on Monday she spends three pound 50, and I know how much less she spends on Tuesday than Monday, because the question tells me, but on Tuesday she spends 50 pence less.

Here are two ways of representing my question.

Here's what she spent on Monday.

I need to find out how much she had left on Tuesday, and I know that she spent 50 P less than she did on Monday.

So, I can use our generalisation that says, "If the minuend is kept the same and the subtrahend decreases, the difference must increased by the same amount." So if my subtrahend has decreased by 50 P, then I need to increase the difference by 50 P.

Here it is with jottings as well.

The minuend stayed the same, the subtrahend decreased, so the difference increases.

I can see a pattern developing in these questions now, with the increase or decrease and the subtrahend being reflected in the change, in the difference.

But let's try one more example, just to be sure.

Here's a question for you to do by yourself, which asks, how much money did she have to put into her savings on a Wednesday? Pause the video while you work this out, using a part whole model and jottings again.

See you in a few minutes.

Welcome, again.

How did you get on? Well, if on a Wednesday Leah spent 70 pence less than she did on Monday, I can use my generalisation again to help me work out how much she had left on Wednesday.

So, the minuend stayed the same, the subtrahend decreased, so the difference must increase by the same amount.

So, the amount that she spent decreased by 70 pence and the difference increased by 70 pence.

Here it is, shown as jottings.

This means, that on Wednesday, she was able to save two pounds 20.

Is this what you got? Here are the generalisations from our last two lessons which we've been using to answer the questions so far today.

And I think, we could combine them to make one generalisation, so we've only got one to remember, not two.

Let's say it together.

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

Have a careful look at this sequence of equations.

What stays the same and what changes? Can we use our new generalisation to describe the pattern? That's right.

In each equation, the minuend stays the same, the subtrahend increases by one and the difference decreases by one.

Now, what about this sequence? What stays the same and what changes here? It's time for you to have a practise on your own now.

So here's the activity I'd like you to do before the next lesson.

I would like you to create your own sequence or sequences where the change in the subtrahend is balanced by changing the difference.

Once you've done that, ask somebody at home to explain your pattern to you.

You might need to help them, and if you do, use our generalisation that's on the slide here.

Now, don't just change the subtrahend by one each time.

Explore what happens if it changes by a different amount.

What happens to the difference then? Be creative.

Try increasing or decreasing the subtrahend by two, three or anything you like.

Have fun.