Lesson video

Hi everyone.

Miss Jones here.

Today's lesson is about Factorising Expressions.

Which I'm really looking forward to getting started with.

But before we can begin.

Please make sure you have a pen and some paper.

As well as removing any distractions and trying to find a nice quiet place to work.

Pause the video to make sure you got all of the ready.

OK.

Hopefully we're ready to begin.

So, for the first task, what I would like you to do.

Is fill in the blank spaces.

So for example I have 144 here and I would like to know what multiplied by what could equal 144.

Now there are lots of different answers we can get for each of these.

So have a go with as many as you can.

What I would really love for you to do as well is to draw an array to represent each equation.

So for example.

If we had 144 and we were to choose the product 2 lots of 72.

If you could draw an array to show that.

Then maybe we had.

2 lots of 72.

Guess it's 144, or another array you can think of again there's lot's of different combinations we could use.

So pause the video here to have a go at that.

So here are some solutions but again there are lot's of possibilities.

So, an example is 12 multiplied by 12 makes 144.

Here we had 2 lot's of 99 was hopefully the most obvious one because we do have two lot's of 99.

Here we got 3a of 3a which is 2 lot's of 3a equals 6a.

And here we have 3 lot's of 11 add 3 lot's of 19 if we use distributivity here.

Hopefully some of you noticed.

That that mean's I've got 3 lot's of 11 add 19 which is 3 lot's of 30.

So this brings us to our connect task.

Where were learning about Factorising.

We can factorise a number or expression by writing it as a product of two or more factors.

What does product mean? Multiply.

When we multiply two things together we get a product two or more things together we get a product.

Brilliant.

Of two or more factors.

So when we were looking at 144.

We had factorised it by writing it as a product of two or more factors so when I did this example.

That is a product.

And that is being factorised but.

What we are going to be looking at say is factorising expressions.

So we have an expression here.

Help these students to factorise 6 add 4n and that is what we're going to do.

Carla is saying, can I put these into equal groups.

So she is represented them using our blocks and our squares that we've seen before.

So she's got 4n's, 4 blue n's and 6 one's if I was putting these into equal groups I'd be thinking.

What can I split 6 and 4n into.

And hopefully we can recognise a common factor of 6 and 4n is 2, so we can split these into 2 equal groups.

And what we have here, is 2 lot's of what? What is in each group.

3 add 2n Good, and remember We're going to need brackets around there.

So that we just don't do the 2 multiplied by 3 first.

Extra points if you've noticed what is potentially not quite right about this expression I've created here.

Cause we don't need to multiply sign, there do we? we've gotten that before.

And we have factorised that using our blocks to help us.

If Xavier is using array to help him out.

So we got 6 and we got 4n here.

Separate things.

On the outside on the left hand side we need to put the common factor of both which we have already discussed.

Is 2.

Then I need to think what would I multiply 2 by to get 6? 3.

What would I multiply 2 by to get 4n? 2n.

So you might have noticed this is very similar to expanding but actually it's in reverse.

So again we get 2 lot's of 3 add 2n.

And that would be our factorise expression.

At this point If you're struggling a little bit with how to find a common factor.

Just write out the factors of both and then find one that's in both of those factors.

No it's your turn to have a go.

To factorise the following and represent them in similar ways.

Just to check that we understand how to do this.

So you can use objects around your home you can draw these out or you can use an array.

But practise both ways to make sure you understand both of them.

Pause the video to have a go with that.

And this is what we should have got we should have got 4n add 8, we could have written this 4 lot's of n add 2, or 2 lot's of 2 and add 4.

So we could factorise them in both ways.

This one is what we tend to see more often because this has been fully factorised.

Cause we've taken the highest possible common factor out.

The 15 add 9m.

We should have got 3 lot's of 5 add 3m.

Really well done if you manged to get that.

Now pause the video to complete your independent task.

The first question was about filling in the gaps to make all of these equivalent.

Hopefully you saw that we have 1, 2, 3, 4, 5, 6 a's 1 2 3 4 5 6 a's there and we have 3 2's.

You should get fill out that.

So that help's out with this one because I know I got 3 lot's of 2 and we just talked about having 6 lot's of a, etc.

For number 2.

You are to factorise the expressions.

And you've been given some clues to help you make a start.

So here we knew that we will split them into groups of 3 or taking 3 out our array.

And then we can fill out the rest.

And here are our answers.

Really well done if got those right.

Now for our Explore task.

We've talked about factorising we can do it in different ways.

Sometime there more than one or two common factors.

So.

We have 4 lot's of n add 2 here That's we've been given.

And what we are trying to do is trying to factorise it in another way.

So in order to do that.

Quite often the simplest way is to expand it first and we know how to expand it so I got 4 lot's of n add 2 which means I got 4n add 4 times 2 is 8.

Here.

OK now, then go and find a different common factor 4n add 8.

We've already done 4's we can't do that.

So we think about our factors of 4n add 8 And that could be.

2.

It's worth noting here actually that when you are writing out your common factors you'll notice that one is a common factor for everything.

And we don't take that out because if we did if we took one out of this.

I'd just be left with the same thing.

Inside the brackets.

So there's no point in doing that.

And it's a waste of time to have that one there anyway we don't needed that.

So, as I was saying we've taken 2 as our common factor this time and so if I've got 4n add 8 in here.

I can find that.

To get from 2 to 4n I need to multiply by 2n and 2 lots of 4 makes 8 so we can factorise it in this way.

So I would like you to do something similar.

With the 3 at the bottom.

Remember drawing those arrays are really really helpful in helping you see these and visualise it and making sure that you don't miss out any steps.

So pause the video to have a go at that.

And here are some of your answers.

So these are the different answers that we could have got.

So for this one for example 6 lot's of n subtract 3.

If you were to expand that 6n subtract 18.

And factors of 6n and 18 we could have got 3.

And going through that process or we could have used 2 and gone through that process.

This last one is very interesting.

Because actually.

Some of you may have noticed and really well done if you had.

That we got a little bit of distributivity going on here because if you would imagine that this bracket here 2n add 1 and 2n add 1 here, imagine that was just A.

If I told you what's 3a add 7a.

You would tell me that's 10a.

And it's no different here 3 lot's of 2n add 1 add 7 lot's of 2n add 1, is 10 lots of 2n add 1 which we can see here.

And that can be factorised again in lot's of different ways.

So really well done if you made that connection that's quite complex stuff so really well done for that.

And really well done again if you got any of those answers.

Brilliant job today.

That brings us to the end of the lesson.

So do make sure that you have an opportunity to do the quiz to check your understanding.

And really well done from me.

Again.