Lesson video

Hello everyone.

How are you today? I am Miss Brinkworth, and I'll be doing this set of maths lessons with you, which are all about multiplication and division.

To start this session on multiplication.

We're looking at the relationship between multiplication and division in this lesson.

So, please make sure you've got everything you need, which is just a pen or pencil and something which you can write on.

And we'll start with these Star Words.

So, I'm going to say them, and if you could say them at home, that would be wonderful.

So, we have multiplication, array, Commutative, times, Equal parts, Whole, product.

Let's just have a look at those words in a bit more detail.

So, I'm sure a lot of this you've seen before.

So, we'll be focusing on our multiplication today, that can be called our times tables or timesing as well concept.

So, often when we're talking about multiplication, we are getting into a Whole, and then splitting that into Equal parts which are two more of our key there.

Product is what we end up with when we times something, we get our product.

And then we have array, that's a way of representing multiplication, which I'm sure you've seen before.

And then we have commutative, which is a nice, long word, commutative, commutative, commutative.

And it's going to be our focus for today, if you haven't had that word before, you're not sure what it means, don't worry, we're going to talk about it in this lesson.

Okay.

Well, what is being represented here? pause the video if you'd like, and just let me know what you think is being represented here, there's no right or wrong answer.

So, this is an array.

This is a way of we can represent multiplication.

So, if we look at this again, here which is in the top of our page there we can split this in different ways, we can split it firstly, down.

So, we could say that we've got four sets of three, or we could split it across, and we could look at having three sets of four.

It's exactly the same picture, the same array, the same number of the dots, but we've split them up differently, into four, groups of three or three groups, of four.

And this is what we mean when we talk about commutative.

We can.

this array can show us different things.

It can show us all these different facts.

So, we have 12 dots there.

So, we can say that 12 is equal to four times three.

Each row is four the dots and we have three of them, four times three is 12.

And it's also true then that three times four is 12.

So, we have four columns, they've each got three in them, so three times four is 12.

It's also true then that four is the same as 12 divided by three, and, 12 divided by four is three.

Have a look at all those facts that are represented there.

And can you see in each sum, it's the same numbers being used.

We only have 12, and four, and three.

They move their position in the sum.

And this is our learning for today.

And this is really useful because it's about making those connections in maths.

If I know this, then I know this.

If I know that 12 is four times three, then I also know that 12 is three times four.

If I know that four times three is 12, then I know if I divide three by four, sorry, if I divide 12 by four, I get three.

So, we can make those connections and we can use our known facts, I'm sure you know your three and your four times tables pretty well by now, to help us with new sums. Let's move on then.

Here's another way in which that fact, three times four is 12 can be represented.

We can have three nests, sorry, we can have four nest with three eggs in each.

We've got those red array of dots at the top there, we could also have like a pothole model where we've split up a bar into four and each one could represent three, or we can have it on a number line as well, where we have three jumps of four.

It's really useful to draw pictures and show different representations in maths.

Okay.

Here we are again then with this idea of commutativity.

So, this shape is the same, it's just been turned on its side.

So, from this we could bring different facts out.

We could say that that top line those top lines have got different numbers in.

So, the purple one there has got five in that top line, and the blue one's got six.

And all that's happened is we've sort of taken our purple shape and sort of twisted on his side.

It's got exactly the same number of squares inside it, but it just changes the facts slightly, five times six is 30.

So it's also true that six times five is 30.

If you look at those bottom numbers there, 30, divided by five and 30 divided by six.

What do you think the missing numbers might be there? Six and five.

So, just like in our last example, we have the same numbers being used all the time, 30, five and six, but that facts, they're just moving their place in the sum.

Okay.

Your turn then, have a look at this, it's six times seven equals 42.

Can you try and find three more facts for me? So, I want one more multiplication fact, and two division facts for me please.

Pause the video here and have a go.

How did you get on? Let's have a look at what you should have had.

And so we've got just swapping six and seven round, six and seven is 42.

So, if there are other multiplication fact, seven times six is 42.

And then for our division fact, 42 makes its way to the start of the sum.

So, 42 divided by six is seven and 42 divided by seven is six.

Well done if you could see all of those.

Now, 42 makes its way to the front of the sum for our division questions.

When we divide, our number is getting smaller.

So we start with the biggest number.

Just moving on then have another go at this one.

What fact do you think is being shown in this array? And what other facts could you see? So, have a look at this figure in the bottom there, which one matches this array? which one is the line going to go to? And then can you find the other three facts as well? So those are multiplication facts, so, when you've decided which one the array shows, can you find me one more multiplication and two division facts please.

Well done, if you could see that this array is showing three times six.

We've got three dots going down the side and then they represent.

they've got six in each row.

And then the other facts for that, well done if you could see all of these, if three times six is 18, then six times three is 18 and 18 divided by three is six and 18 divided by six is three.

And you can see again that large number that was at the end when we'd multiplied, is now at the beginning when we divide.

Okay, have a go here.

Can you use your multiplication knowledge to fill in these gaps from this simple multiplication fact, can you find the multiplication and the division that goes with them? How did you do? Hopefully nice, simple one here, to just swap two and three round also equals six.

And then remembering that, that larger number, makes its way to the front of the sum for the division questions.

But we use exactly the same numbers.

If a new number is popping up, you might need to go back and just have a check that you've got that right.

And drawing can always help, I find.

So, you're never too old to just draw out what you think is being represented here.

So this little array would only take a moment to draw, six circles, and then you can see that you've got, two lots of three and three lots of two.

And it's really helpful to have that there, to find these other facts.

Okay.

Be careful when we're talking about division.

So, it's true that 10 divided by five is two, but, it's not true that five divided by two is 10.

So, be careful, you can't just put the numbers whether you like, it doesn't work quite like that with division.

So, remember that the big number has to be at the front of a division question and numbers get smaller as we divide them.

So that's a really good way to check your division questions are correct.

If you've ended up with a bigger number after the equal sign, it must be wrong because we kind of shared it if we've ended up with a bigger number.

But that one at the bottom is true.

We've got our biggest number 10 at the start, half of 10 is five.

So, just a warning that to be careful and check your division questions carefully.

And there's a nicer way that you could draw it out and just check.

Yeah, I've got 10 there, and if I circle, I've got five circles.

So 10 divided by five is two or 10 divided by two is five, but we can't have that one in the middle, that one's not quite correct.

Okay.

Your turn, have a go at the main activity on your own, pause the video and then come back and see how you got sum.

Well done.

Let's have a look.

So, this is draw the representations and then think about what other numbers facts you can find.

So, hopefully you could say that six times one is six and three times three is nine.

Your other number facts then, six times one is six, six divided by one is six.

And, you could also have six.

what else could you have? Yeah.

because you got two sixes there, So those are your facts for that one.

And then for your other one, for nine, you can have nine divided by three is three, and then again you could draw out your array to help you with that one as well.

So well done if you saw that.

Really good.

Okay.

Matching the facts then.

So, which ones are related? This is nice and easy if you can see the same numbers reoccurring then the facts must be related.

So we have two times nine is 18, and so 18 divided by nine is two, 24 divided by six is four and so four timesed by six is 24.

And then here we've got this one with 35 at the end, when it's a multiplication question, I'm moving it way to the front for that correct division question.

Well done if you could see those, not too hard to match those ones out I don't think.

Okay.

Lots to fill in here.

And again as long as you can remember that you're using the same three numbers, this should be quite simple for you to work your way through.

So, hopefully you can see that four times three in that array is 12.

We then have three times four is 12.

And then for our division questions, 12 goes to the front, so 12 divided by three is four and 12 divided by four is three, the same numbers reoccurring each time.

So, we've got a similar question here, with two times six is 12 and then six times two 12.

Again, but big numbers go straight to the front now when we're talking about our division questions.

So 12 divided by six is, and 12 divided by two is six.

Really good.

And then for our last one, four timesed by seven is 28, so seven timesed by four is 28, and 28 is seven divided by four, sorry, 28 divided by seven is four, and then 28 divided by four is seven.

Not too hard once you've got the hang of it.

Well done.

Okay.

What was the same and what's different here then in these arrays?.

So, we've got four timesed by three is 12 and four timesed by six is 24.

Well, hopefully you can see that our array has doubled.

We've got the same circle, the same three timesed by four again, and that's because six is double of three.

So, we've doubled our three to six, so, our array has doubled and our answer has doubled, 24 is double 12.

Really well done if you could see that.

And finally, there's other facts that you can pick from 11 times five is 55, hopefully you could see, five timesed by 11 is 55, 55 divided by 11 is five and 55 divided by five is 11.

Really good.

Hopefully, you have found that useful and you feel quite confident now in that commutativity between, the different multiplication and division facts.

So, have a go at that Final Knowledge Quiz and see how well it sunk in.

Well done, lots of new learning there, I'm really, really pleased with how you did.

Bye, bye.