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Hi everyone, Ms. Jones here.

Today we are going to be looking at a bit of a recap of distributivity and how that introduces us to expanding.

So we're going to be doing some more algebra today which I'm really looking forward to doing with you.

But before we can begin, make sure you've got a pen and some paper, you've got rid of all the distractions around you, and if you can, try and find a quiet space to work.

Pause the video now to do that before we can get started.

So the first thing I would like you to do is to copy and complete the following in different ways.

So we have 12 multiplied by 15 here.

And I would like to know how you could fit in these gaps.

So it equals to something multiplied by something add something.

So again, we're looking at that distributivity, trying to refresh our memories of what that is.

If you are happy with that, go ahead and try and draw an array to represent those equations.

If you want a little bit of a hint, then keep listening.

So the first thing I would be looking at is, I know I've got a product here.

So if something multiplied by something.

And I can link that directly to what we've got on the left-hand side of our equation.

So for example, I could put 12 here and I know I'm multiplying 12 by 15.

So I need any two numbers that sum to make 15.

So I'm just going to choose 10 and five.

And that is the array to match it.

So I've got 12, have 10 up here, five up here.

12 lots of 10 and 12 lots of five.

And there's an example of another array.

So pause the video to have a go and create some more examples.

So there are loads of different things we could see.

We got the same as what I looked at before.

We could also almost swap this around use a bit of commutativity and start with the 15.

15 lots of 12 by 10 add two.

You could have had any combination of numbers that make 12 in here.

Any combinations that make 15 in here.

So really well done if you managed to do that.

And especially well done if you manage to represent these as arrays because that's going to be really useful for later on in this lesson.

We can use the distributive property to expand expressions.

Remember what expressions means.

This is an expression.

But this whole thing would be an equation.

So this on its own is an expression and we want to expand it.

So I've got four lots, which I've written here, of n and three.

I've got four lots of n, therefore, which I've put here.

And I've got four lots of three, separately.

So we are expanding each term one by one.

Four lots of n and four lots of three.

A classic mistake here and a classic misconception is people forgetting to multiply both of those things.

So, are lots of people that just get the answer.

Oh, I've done for lots of n, that's fine, that's done, add three.

That is not correct.

And that's why writing out or drawing out using these arrays is a really helpful reminder for yourself to multiply both parts of what's inside the brackets, or they might even be three parts of what's inside the brackets.

And it just reminds you that you need to do all of those separately.

We could also represent it in an array using those blocks that were used in a previous lesson.

So here we've got n, and we've got three ones, and we've got four lots of that.

So four lots of n, add three.

That means I've got four n's, and I've got 12 ones.

Four n add 12.

I would like you to expand the following and represent them in similar ways.

And it's really important that you don't skip this step.

I would really like you to create those arrays because they're really, really important.

So pause the video to have a go at that.

So these are the answers.

The first one, we have to remember again, to expand.

Both of these are four lots of three and four lots of n, gets me 12 and four n.

Five n and 15 for this one.

This one is 8 n add 12.

And this one, you'd have to draw it slightly differently.

So, an extra special well done if you managed to represent this cause it was a little bit different.

Because I've got 12 lots of n, and then I'm subtracting it by 12 lots of one.

So this whole thing is going to get me 12 lots of n and then I'm subtracting the 12 at the end.

So that gets me 12 n, subtract 12.

Amazing job if you managed to do those and extra points if you drew all of those arrays as well.

Pause the video to complete your independent task.

So, for the first question you needed to, we're just working with numbers here.

No algebraic terms, just numbers.

And we're using the distributed property to complete the statements.

So, hopefully the same concept applies with expanding.

You've got three lots of 10 and three lots of two.

And similar with the other ones as well.

For these ones, hopefully you drew yourself an array that looks a lot nicer than mine.

So you've got nine lots of n.

Nine n.

And then you've got nine lots of three.

So, we've got our final answer here.

Amazing job if you managed to get all of those right.

Well done.

Our final task.

We're going to be moving horizontally or vertically through this grid.

The starting point is here.

You can only move horizontally.

So when I'm talking about horizontally, think like horizon and we're going this way or vertically, up or down.

So I can only go to this one, this one, or this one to start off with.

But, I can only move to equivalent expressions.

So, think about, can I move to this one? No, because if I were to expand that, I would get eight n but I'd get a number much larger than 16 if I did eight multiplied by 16.

So it's not that one.

Is it 24 n? Well, if you remember, we cannot just combine n's and ones together.

If we had those blocks and they're separate things.

We can't just go, "Oh, that's 24 n." It doesn't work like that.

They're separate things.

Whereas, for this one, if I were to expand this, it'd be eight n, add 16, so it would work.

So the only way I, directionally I can go, is down.

And then from here, I can only go vertically or horizontally remember.

So you're trying to get to the other side of the grid.

Pause the video to have a go at that.

If you manage to get to the other side, amazing job, well done.

This is what we should have got.

And this is the direction we should have been going in.

So really, really good job is you managed to get through all of those.

That's absolutely brilliant.

And that brings us to the end of the lesson.

So again, a massive well done for all of your hard work today.

You've been brilliant.

And make sure you complete the quiz at the end.

See you next time.