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Hello, and welcome to today's lesson about Array Models.

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

Please take a moment to clear away any distractions, including turning off any notifications.

Finally, if you can try and find a quiet space to work where you won't be disturbed, okay? When you're ready, let's begin.

Okay, so let's try this task.

I'd like to pause the video and have a go.

Pause in three, two, one.

Okay, so hopefully you've had a go and hopefully you've managed to get a few.

Now I'm going to start with the one that I think is super easy, but people always forget this one, and I don't want you to forget this one.

One times 36.

And because we've got that, we're allowed this, 36 six times one.

They are commutative, okay? One times 36 equals 36 times one.

That property is called commutative, okay? And I want you to remember that word 'cause we're going to be using it a lot.

So we've also got two times 18 and 18 times two.

Why? Because multiplication is commutative, the order does not matter.

Okay, so we've got one, two, does three go into it? Yes, it does.

Three times 12, okay? Which means we've also got 12 times three because multiplication is commutative.

Does four go into it? Yes, it does.

Four times nine, nine times four.

We can have that one because multiplication is commutative.

Good.

Okay, so one, two, three, four.

Now notice I've done it like this, I do it like this, so I don't miss any, okay? And let's check five.

Does five go into it? No.

Does six, yeap.

How many times? Six times.

Okay, so we've got six times six.

And, well, I don't need to write that again because you know, six times six is obviously six times six.

So I don't need to write that one again.

And now I've got the next one would be seven and eight and nine.

But as soon as I get to the same number twice, or as soon as I get to two numbers next to each other, I don't need to keep going, all right? So here I've got one, two, three, four, eight, nine different ways.

Did you manage to find all nine? Did you try for some non-integer values? If you tried for some non-integer values, you might have had something like this, a half times 72 or 0.

25 times 144.

Hmm, is there more? Yes, there's lots more.

In fact, there's infinitely many, okay? If we include.

Oh, I didn't mean to cross out.

If we include non-integers, there's actually infinitely many answers, which is a really tricky concept to get your head around, but it's one that I find very interesting.

20 cubes have been arranged into a rectangular array.

The array shows that 20 equals four times five, because there are four rows.

So four rows of five cubes.

Can you see that? But can you also see, there are five columns of four.

So we also have five times four equals 20.

Okay, so we have both of these.

We can have a look at rows and columns and either way we get 20.

And that is really important.

And you might think of some division calculations as well.

20 divided by four equals five, okay? If we have 20 squares or 20 cubes and there are four rows, how many are on each row? Or you might have 20 divided by five.

If there are five equal columns, how many are in each column, okay? So there are some ways that you might want to think about it.

Now we're going to be focusing a lot on this property, the commutative property today.

So commutative.

I'd like you just to pause the video and have a read and try and make sense of this slide.

So pause in three, two, one.

Okay, so commutative.

This is all about commutative.

Now, can we see this? Here we've got three by five, three times five equals five times three.

Here we've got three by six, three times six equals six times three.

We can think of it as an area model, okay? Three times five, 15, five times three 15, same answer.

But not only is multiplication commutative, so is addition.

Five plus three equals three plus five.

Just what it means, is that the order doesn't matter.

So for multiplication and addition, order does not matter.

However, for subtraction and division order does matter, okay? And you can see in this bottom corner there that 15 divided by three does not equal three divided by 15, and 15 subtracts three does not equal three subtract 15, okay? So which two operations are commutative? Multiplication and addition.

Okay, and we can use this property to work up other facts.

So if I know 91 times 53 equals 4,823, what else do I know? So pause the video if you need more time answer in three, two, one.

We know 53 times 91 that is equal to 4,823, okay? So the order has just been swapped, so the answer is going to be the same.

Okay, so now it's time for the Independent Task.

So I would like you to pause the video to complete your task and resume once you finished.

Okay, so here are my answers.

You may need to pause the video to mark your work.

And question number two.

Okay, so just on C, don't forget about those division calculations as well.

Okay, and now it's time for the Explore Task.

So this is similar to the task that we did at the start, the Try this Task.

The array below represents the number 24.

Write fact families for this array.

So write as many different calculations as you can see.

What other arrays could we draw for 24? And that's the part that's similar to the start, okay? Write a fact family for each of these arrays.

Okay, so I'm going to give a hint in a minute, but I'd like you to have a go first.

So pause the video and have a go, and if you need to, come back for the hint.

Okay, so here is my hint.

Here are all the different arrays that I can draw, okay? And you need to write the fact families for each of these.

So my fact family for this, there should be four calculations for this one.

I have four times six equals 24, six times four equals 24.

Okay? So now have a go and find the rest of them.

And here are my answers.

Pause the video and mark your work.

Pause in three, two, one.

Okay, and that is it for today.

If you'd like, please ask your parent or carer to share your work on Twitter tagging @OakNational and #LearnwithOak.

Thank you very much for taking part in today's lesson, I look forward to seeing you next time.