Lesson video

Hello everyone, I'm Miss Brinkworth.

I'm going to be going through this math lesson with you today, which is all about everybody's favourite, multiplication.

So should we look at today's learning objective? What we're going to be doing is we're going to be using factors and products to solve division problems. But Miss Brinkworth, you just said it was all about multiplication.

Well thankfully, for division, we're always utilising our known multiplication facts.

So today's lesson is going to using what you already know, a little bit of new key vocabulary, we can see factors and products there in our learning objective.

But don't worry, we're going to go through all that together.

And we're going to be applying it into a new context today.

So let's have a look at our lesson agenda.

We're going to recap on those fact families.

Those are those numbers that have that division and multiplication relationship.

And if we can remember those relationships, it makes answering a whole list of questions really, really simple.

What else are we doing? We're going to explore factors, multiples, and products.

That might be new vocabulary to you, but don't worry.

Thankfully, it's things you're already aware of, we're just going to give it a new name.

We're then going to have a go at applying that to some word problems. And then at the end of the lesson, you've got that independent work and exit quiz, just to check how far and how well today's learning's gone in.

So let's get started.

All you're going to need is a pen or pencil, and some paper.

A big smile will go a long way.

So pause the video here and just get what you need.

Okay.

Lovely to have you back.

Let's get started straight away.

So here's your warm up.

It says which fact family, which fact is missing from this fact family? So you can see that those three calculations there use the same three numbers, 3, 7, and 21.

Those three numbers have a very close relationship.

And you can pull different facts from them.

There are three there, but without changing the numbers, can you find one more for me? Pause the video and take as long as you need.

How did you get on? Well hopefully you can see that there are already two multiplication questions there.

You've got 3 x 7 is 21, and 7 x 3 is 21.

We've also got one division question there already, 21 ÷ 3 is 7.

Now we know that that division question is correct because we've got the whole, the larger number, at the start of the question, and we know that 3 and 7 multiplied together give us 21.

So if we switch that around for its inverse, if we share 21 between 3, we get 7.

And hopefully you know that you can also change it so that you've got 21 ÷ 7 gives you 3.

Okay.

So well done if you found that missing fact.

So you can see here that with one simple multiplication bit of knowledge, you can pull those four facts, two multiplication and two division.

So well done if you got that one right.

Okay.

So here are some arrays.

Can you see what is the same and what is different about these? So have a think about what they've all got in common and what they've got that's different.

Pause the video and have a go.

Okay.

Let's see how you got on.

So hopefully you can see that what is the same with all of these arrays are they've all got 12 dots.

So they're all showing 12.

What's different is that those 12 dots have been put into different groups, different shapes.

So we've got a different number of columns and rows that those 12 have been put into.

So this is a really nice way of showing what our key vocabulary is all about today.

So we could see these as multiplication questions where the answer is 12.

To all of these multiplication questions, the answer is 12.

And that is the product.

When we take two numbers, multiply them together, the product is the answer.

The product is where we've multiplied two numbers together.

I think about that is product is something you make.

So if you've been working hard all afternoon in your writing lesson, your product, what you've got at the end of it, is a lovely story.

If you've been in the kitchen cooking up a storm, maybe the product that you've got at the end of it is a cake.

So the product is what you make.

The product in math is two numbers multiplied together.

But what's different is how that 12 has been got to.

So you can see that one on the side there as 2 x 6.

So two lots of 6 = 12.

The one at the top there, you can see as four lots of 3, 4 x 3 is 12.

And the long, thin one, we could see as 1 x 12.

So in each group there's one and there are twelve groups.

Those are factors.

So the pairs of numbers that we multiply together to get the product are called factors.

Factors normally come in pairs because we're normally multiplying two numbers to get our product.

So there's our product and our factors.

So have a go at this.

Multiples in this question is similar to products, what we get when we multiply two numbers together.

And these two little creatures are saying all multiples of four are multiples of two.

And the other one is saying all multiples of two are multiples of four.

So what they're saying is do all the numbers that are answers in the two times table also come up in the four times table? And do all the answers from the four times table also come up as answers in the two times table? Pause the video here and let me know what you think.

Well done.

Let's have a look at this together.

So all multiples of four are multiples of two.

So all answers in our four times table are also answers in our two times table.

Well let's check.

Let's go through a few of our fours.

4, 8, 12, 16, yes those all come up in our two times table as well, don't they? So that first little creature is correct.

What about the second one, then? All multiples of two are multiples of four.

So all answers in our two times table are also answers in our four times table.

Let's check.

Multiples of two, 2, 4, 6, 8, 10.

Well some of those come up in our four times table, 4 and 8, but not 6 and 10.

So that one's not always true.

So it's just interesting to think about using that vocabulary correctly.

Okay.

How about this one then? Is 10 a multiple of 3? Does 10 come up as an answer in the three times table? Can 10 be equally shared into three groups? Well let's have a look.

Let's check.

One, two, three.

There's our three groups.

Let's share our ten.

Four, five, six, seven, eight, nine, and we've got one left over.

So we can see there that 10 is not a multiple of three.

Ten is not an answer in the 3 times table.

That one's not true.

Okay.

Let's have a go at this.

I've written your turn, but actually we're going to do these ones together and then you can have a go.

20 is a multiple of 3.

Is 20 in the three times table? Well we just saw that 10 wasn't, and we know that 20 is double 10.

And we also know, hopefully you know, that 21 is a multiple of 3, because 3 x 7 is 21.

So no, 20 is not a multiple of 3.

12 is a product of 3 and 5.

That would mean that 12 is the result of multiplying 3 and 5.

Let me check.

Three lots of 5, 5, 10 15, not 12.

So that one has not used product correctly there.

8 is a multiple of two.

Does 8 come up in the two times table? Yes it does, doesn't it? 2, 4, 6, 8.

Four twos are 8.

10 is a product of 4.

Can we do something to 4? Can I multiple 4 by something to give me 10? 4, 8, 12, nope, it skips out 10.

So that one's incorrect as well.

And well done if you could see that.

Okay.

Now it is your turn.

So pause the video here and let me know if you think these statements are true or false.

Okay.

How did you get on? Let's have a look together.

2 and 3 are factors of 6.

Can we multiply 2 and 3 together, or 3 and 2 together, and get 6? Yes we can.

That one's fine.

24 is a product of 4.

Does 24 appear in the four times table? It does.

I know that 20 is in the four times table.

Because I'm very confident with my fives, and I know that 4 x 5 is 20.

I just need to add another 4 on to that, which means it must be a product of 4.

So yep, that one's fine.

8 is not a multiple of 2.

Nope, that one's incorrect.

We know that 8 is a multiple of 2, 2, 4, 6, 8.

We checked that in the last slide didn't we? So that one's not correct.

And 13 is a multiple of 3.

Again, that one is not correct.

But why do you think people make that mistake? Why do you think people think 13 might be a multiple of 3? Well I think what happens is people think that because there's a three in the number 13, it must be in the three times table.

But that's not how it works, is it? We know that.

We also know that 12 is in the three times table, so the number just next to 12 can't also be in the three times table.

Well done if you saw that.

Okay.

So how many different ways can 20 coins be split? When we've worked this out, what we'll have is all the factors of 20, the pairs of factors that we can multiply together to get 20.

So can I split 20 into a group of 1? Yes I can.

If I've got 20 and I want to share it with one person, and just give it to one person only, then yes of course we can.

We can, any number is divisible by 1.

Any number can be divided into a group of 1.

Can 20 be divided into a group of 2, into 2 groups? Yes it can.

And each of those two groups would get 10.

We know that because 20 is an even number, so it can be divided, it can be divided by 2.

What about 3? Does 20 appear in the three times table? We've looked at that one already, and it doesn't, so we'd skip on to the fourth.

And again, I feel very confident with my fives, so I know that fact 4 x 5 is 20.

And so that corresponds here, as well, with 5 x 4 is 20.

Six, no, six, 20 doesn't appear in the six times table.

I know that 18 is in the six times table and 20 is only two more, so I haven't made another jump of 6 to get from 18 to 20.

So that one can't be.

And again with my sevens, I know that 21 is in the seven times table, so 20 can't be.

I'm going to stop there because that's, I know that that's where it stops there, my factors of 20.

So if I move on to the next slide, you can see that what we've found here are our factors of 20.

These are the pairs of numbers that we can multiply together to get the product, which is 20.

So 1 and 20 can be multiplied together, 2 and 10, 4 and 5, and in, obviously, in whatever order.

We know that we can do them, we can do multiplications in any order.

Okay.

Your go, then.

How many different ways can you split 7 coins? If you have 7 coins, how many equal groups, how many different ways can you split it into equal groups? Think about multiples, think about factors.

Have a go.

Okay.

Let's see how you got on.

So 7, 5, 6, 7, seven's quite a special number, and maybe you saw this.

It cannot be split equally into very many groups.

You could, you can split it into 1 or 7, and that's it.

So you can have 1 group of 7, or you can have 7 groups of 1.

So if you had 7 people, they could share 7 equally.

Of if you just kept them all to yourself you could have 7, and that would be just with 1.

That makes 7 a prime number.

There are lots of different prime numbers.

Three is also a prime.

And they're a very interesting number.

So when we're talking about how we can split numbers up, 7 is a prime number.

It can only be divisible between itself and 1.

Okay.

Time for your independent task.

So pause the video and come back for the answers when you're ready.

Let's see how you got on.

So we had some more of these, these questions about whether numbers can be split equally.

So can 8 be shared equally between, between 5 people? How do you know? No it can't, because 5 is not a factor of 8.

8 does not appear in the five times table.

Can 4 people get an equal number of 12 coins? Can 12 be split equally between 4? Yes it can.

3 x 4 is 12, so each people would, each of the 4 people would get 3.

So 4 is a factor of 12.

How many people can share 15 coins? If you have 15 coins, how many people can share them equally? Well, quite a few different kinds of groups actually.

Like any number, it can be divisible by itself.

So 15 people could get 1, or one person could get 15.

So we're always going to have 1 and the number itself.

But 15 also appears in the three times table and the five times table, so that's another factor pair for 15.

Is 9 divisible by 2? Can 9 be split equally between 2 people? No it can't.

9 is an odd number, that means it cannot be equally split in half.

And for your challenge, if 6 people share 13 coins, how many will be left over? Well, hopefully you could see that 2 x 6 is 12.

So we've got close to 13, but there's one left over.

Okay.

How can these coins be split equally? So what you're looking for is all the factors of these numbers.

And really, really well done if you found all of these.

So for 16, you could have all of these numbers.

For 32, you could have all of these.

For 9, you could have all of these.

And for 21, you could have all of these.

So well done if you recognised all of the times tables that those numbers appear in.

Really, really good work.

And finally, a sort of riddle.

How did you work this one out, I wonder? Did you think of a number and work out whether it met all the statements? Did you cross some off as you realised that they weren't quite right? Did you think that you needed to look for a bigger number or a smaller number? I would be really, really interested to see your working out for this question.

Even if you got it wrong, that's absolutely fine.

Now I got the answer 50.

I'm not saying that that's the only right answer, but it certainly meets all those statements.

So well done if you got that as well.

Like I say, I would love to see your work and all of your working out from today's lesson.

If you'd like to share it, talk to a parent or carer, ask them to share your work on Instagram, Facebook, or Twitter, tagging @OakNational and #LearnwithOak.

But please, before you go, have a go at that exit quiz, that final knowledge quiz will be a lovely little chance for you to see how well today's learning's gone in.

You've all worked fantastically hard on today's new vocabulary and new context, so well done.

Enjoy the rest of your learning today, everybody.

Bye-bye.