Lesson video

Hello and welcome to today's lesson on multiplication facts.

For today's lesson, all you'll need is a pen and paper or something to write on and with.

If you could please take a moment to clear away any distractions, including turning off any notifications, that would be great.

And if you could find a quiet space to work where you won't be disturbed, that would also be brilliant.

Okay, when you're ready, let's begin.

Okay, so I'd like you to have a go at the try this task.

And before I ask you to pass it, I'd just like to read this out, just so you get a sense of what we're doing.

Okay.

We can find the 4 times table from the 2 times table.

4 x 7 = 2 x 2 x 7, which then equals 2 x 14, which equals 28.

Now I want you to think about what we've been doing in previous lessons and see if you can understand where that comes from.

And then see if you can understand the two statements below.

Okay, so when you're ready, pause the video in three, two, one.

Okay, so we're not going to go over on this slide.

We're going to go over it in the next few slides.

And the reason why is because I really want to break each concept out.

So we've got the associativity, distributivity, and commutativity, okay.

They are called the axioms and we looked at them in previous lessons and they are super important in mathematics, okay.

So they are the axioms. Okay, do you remember what all three were called? Associativity, distributivity, and commutativity.

Okay, do you remember what they do? Hmm.

Okay we're going to be using associativity first.

We can find the 4 times table from the 2 times table.

So that was like the one we had before.

So now imagine I've got 7 x 4, okay.

So that was one we had before.

I can't remember if it was the other way around, but it doesn't matter because it's commutative.

So the order doesn't matter.

And what we can say is we can say that four is the same as 2 x 2.

So we get this.

All right, now associativity says it doesn't matter which multiplication we do first.

So I'm going to say, let's do the 7 x 2 first, rather than the 2 x 2.

Which gives me 14 x 2, which I know how to double.

So that is 28.

Okay, and we can actually do that for not just four.

We can do it for lots of different numbers.

So if it was 7 x 6 and you didn't know your 6 times tables, you can split this 6 off into 2 x 3, and then you might do 7 x 2 to get 14.

And then times that by 3.

Or, you might do 7 x 3, and then times that by 2.

So there's different ways that we can do calculations.

If it was 7 x 8, we might want to split the 8 into a 4 and a 2.

Or, we might want to split the 8 into 2 x 2 x 2.

Okay, how about this one, I can half the 10 times table to find the 5 times table.

Hm.

Well say let's do seven again.

Say I was doing 7 x 5.

Now I can write this like this because 10 times a half, a half of 10 is 5.

And now I can do 7 x 10 first and then half of 70, 35.

Let's check.

Well, that's 28 + 7 is 35.

So we know that that's definitely correct.

Okay, have a think, how could we use associativity for the 9 times table? Or the 12 times table? Okay, you might want to pause the video just before I talk through it.

Okay, so hopefully you paused it and had a think now 9 is 3 x 3.

So we could use that.

12 is 2 x 6 or 3 x 4.

So we might want to break it down that way.

Or 3 x 2 x 2, even.

Okay.

How could we use distributivity in the times tables? Well, say I was doing yeah, let's do 8 x 7.

Okay.

Now what I'm going to do is I'm going to split this seven up.

5 + 2 is 7.

Okay, so I haven't done anything wrong here.

Now what the distributive property says is that that is the same as this.

Can you write, remember from a array diagrams that showed that this was true.

So now I can work out 8 x 5 and now I can work out 8 x 2.

Okay.

So the distributive property splits one multiplication into the sum of two multiplications and it's just used to make things easier.

So if you don't know your sevens, you can split that 7 up into a 5 and a 2.

And this property is really important.

Okay.

It's used throughout secondary school.

I can use the 10 times table to work out the 9 times table.

Okay.

Well, what's going on here? Let's do it again.

How can I get 10 from this? Does it work with subtraction? Yes, it does.

Okay.

And I've just used here, distributivity to work it out and that made the calculation a lot easier for me.

It saves me having to learn my 9 times tables and I can just do my 10 times tables.

Take away that 1 of that number.

Now do I think it's a good idea to learn your times tables? Yes.

It means that you can do certain calculations faster.

However, it's really important that you can understand how calculations are related and how we can break them down.

And it's particularly important when we get to algebra.

Okay, so I just want you to have a think.

So maybe pause the video and have a think.

Okay, so hopefully you've paused the video.

How could we do our eights? Well, we could do 5 + 3.

Or, we could do 10 - 2.

So we could do an addition one or a takeaway one, depends what you prefer.

How could we do 12? Well, I think that the easiest way that I think for 12 is 10 + 2 and split it that way.

Okay, what's going on here? Well, Xavier is asked whether he has to memorise both 6 x 8 and 8 x 6.

Does he? No, he does not.

Let's have a look why.

Okay.

I'm 6 x 8 = 48, 8 x 6 = 48.

They are exactly the same.

Why are they the same? Can you remember which axiom it was which tells us they are the same? Commutativity.

Okay, hope you got that.

All right, so they are commutative.

And what commutativity does to our times table facts is really awesome.

Look at this.

Boom.

Okay.

We only have to remember just over half the facts now.

It's gotten rid of all this massive chunk.

Can you see what's just not quite relevant to a commutativity.

Can you see what's going on down here? What's special about these numbers? Do you know what they're called? They are the square numbers.

Okay, so now I'm going to use the axioms to try and work out a few different sums. So I'm first going to do associativity.

Well, what could I do here? How could I split this up? There's loads of ways I can see so many at the moment.

Let's do this first.

So that's 6, 3 x 2.

Now I'm going to swap the order so I do the 2 x 15 first.

Well, not swap the order, but I'm going to write a brackets to show that I'm doing the 2 x 15 first.

2 x 15 = 90.

Could we have broke it down a different way? We definitely could have.

Let's do, let's keep the 6 now.

And let's break that down into 5 x 3.

Okay.

Just pretend I'm really good at my 5 times tables, which I am, I'm a math teacher.

Okay, 6 x 5.

We'll do that first this time.

X 3 = 30.

You could have done it a different way.

You could have done a 6 x 3 x 5, 6 x 3, 18 x 5.

Hmm, that's not that nice.

Let's make that into 5, sorry, 10 x a half.

18 x 10 = 180 x half = 90.

So you can see there's so many different ways that we can do it.

And I'm starting, my writing got a bit diagonal there, but it's just, it's such a useful property.

So I'd like you to practise it now.

Okay.

So have a go of this and I want you to use associativity and see if you can do it in two different ways.

Okay, so pause the video in three, two, one.

Okay, welcome back.

Now, my first way, it was like this, split this up into 4 x 4 and then do that first.

So that's 20, 20 x 4 = 80.

Or, you could have done, and I skipped a few steps in my writing in that, because I'm just a bit conscious of space.

So 5 x 2 x 8.

Okay, so that's 16.

And then I'm going to do the 5 x 2 first.

Cause I want to make 10.

Cause 10 is quite nice.

It's a nice, easy number to work with.

So then I've got 10 x 8.

Okay.

Could you have split up even more? Well, you could have, if you'd wanted to, you could have split it up like this 5 x 2 x 2 x 2, Oh x 2, 2 x 2 = 4 x 2 = 8 x 2 = 16.

So you could double five, double it again and again and again.

And you would get the same answer and it's just, it's it's awesome.

It's incredible how many different ways that you could do this and you might have even thought found a way that I didn't do there.

And so really well done, if you did.

You might, oh you might have done that, you might have made that the 5 into 10 x a half and done it that way.

Okay, now we're going to do this again, but we're going to use distributively this time, all right.

So here, I'm going to split this up into this.

Now distribute, the distributive law says that I can write this as the sum of two products.

Okay and product's just multiplication or a word for multiplication.

And we got the same answer as before, but it's just, it's just another way that we could have done it.

And you could have split this up into anything.

You could have split it up into 12 and 3, 20 - 5.

You could have even split the 6 up into 3 and 3 or 4 and 2 or there's so many different ways that you could have done it.

But I just chose this one because I think it's usually easiest if you break something into it's tens and it's ones.

Okay, so now have a go at the alternate one, and I want you to use the distributive property.

So pause the video and have a go.

Pause in three, two, one.

Okay, so welcome back.

Hopefully you've done this all a different way, but hopefully you've got the answer, correct.

And used the distributive property.

Okay, awesome.

Now I want you to have a go at the independent task.

Pause your videos to complete your task, resume once you've finished.

Okay, and here are my answers.

I'd like you to mark your work.

You may need to pause the video.

Okay, so now it's time for the explore task.

So you've got to match up the correct pairs of calculations and there's some blanks that you have to fill in.

Okay, this one takes a bit of thinking, so don't expect to get it quickly, but just before you pause your video, I just want to let you know that I have a hint for this task.

So if you have a go and you are struggling, then you can come back and use the hint.

Otherwise, pause the video to complete your task, resume once you've finished.

Okay, so here is my hint.

I have filled in the two blanks, which should hopefully help you.

It's still a tricky task, but hopefully this just gives you the little push that you need to be able to do it.

Okay, and here are my answers.

Here are my pairs these two, these two, these two and these two.

Okay, this last one.

This last one's quite interesting.

Why are they the same? Because 3 x 3 is the same as 4 + 5.

We've broke that 9 down into a multiplication here and here we've broke it down into a sum.

Okay, and that is all for this, this lesson.

I hope you've enjoyed it.

And I hope you've learned something.

Thank you very much for taking part in all of your hard work.

And I will see you next time.