Lesson video

Hi again everyone.

I hope you're well.

Today's lesson is to identify properties of numbers.

Now before we start on the lesson, I just want to have a think and do a bit of a joke of the day.

So what does the ocean do when it sees its friends? Not sure.

Well it waves.

Yeah I know, good one.

Okay let's get started with the lesson then.

So let's have a look at that lesson again.

The first thing we're going to do is we're going to go back through and we're going to define multiples and factors.

We're then going to think about common multiples of factors, and then you guys are going to apply that in an independent task which is a bit more exploratory and gets you investigating common multiples and factors.

Make sure you've got your pencil and paper ready to go so you can make markings as we go through the lesson.

Now, to get us started I've got four words here and four definitions.

What I want you to do is have a look at the words and definitions and match up the right word to the right definition.

So pause it here now, then we'll come back and have a look at the answers.

Okay how did we do? So we might've started with I think multiple and factor we're probably most familiar with, so a multiple is the result of multiplying a number by an integer, a factor is a number that divides into another number exactly and doesn't leave a remainder.

So 24 is the factors of eight and three, for example, and then, now a bit of a clue here with the ones we've got left, a prime number is a number that can only be divided by itself and one, and lastly a composite number therefore is a number that is not prime.

So anything that has more factors than one and itself.

Okay hopefully you're okay with that.

Let's move on then.

So here I've got some factor bugs and I've got the factor bugs all the way through to 15, but you might be able to see that one is missing.

So why is one missing? Why is it really difficult to draw a factor bug for the number one? Have a think.

Okay yeah, so if I was to do a factor bug for one, well I might struggle because I draw my bug, I write one in, and then I can have one antenna, I have one, but nothing else 'cause yeah, it's on its own.

So yeah, one we don't really do a factor bug for.

Now have a look at the other factor bugs, and I just want you to be observant and see what do you notice about the factor bug above it.

But it's something really simple, don't worry.

Write down everything you can.

Jot down anything.

It might be something that you notice some sort of pattern there or identify something.

So have a think, pause the video, and think what do you notice? Jot any ideas down and we'll see what we come up with.

Okay so some of the things you might've come up with, let's have a bit of a think.

Well first off, we might've said well I can see factor bugs going all the way up to 15.

Okay great, what do you notice about these then.

Well you may have noticed that some of them actually don't have many legs on.

So you can see that all of our factor bugs have got the antenna 'cause they are the factors of one and itself, and all of the numbers will have that.

But then some of them for example two, three, five, don't have any legs whatsoever.

What is it about them that means they don't have any legs.

Yeah right so go back to our definitions, these are what we call our prime numbers.

It means that they're only factors of one and themselves, therefore they're what we call factor slugs 'cause they don't have any legs whatsoever.

So two, three, five, seven, not nine.

What is it about nine that means that it isn't a prime number? Yeah, that's right.

So we can see that nine has a factor of three, but we know that three multiplied by three is equal to nine, but we've only written three here once 'cause it's only a factor once.

So that makes it a special type of number, and can you spot another number there which has a similar thing to that.

That's right, just above it.

Four is the same.

Now what do we know about the numbers four and nine that might make them special? That's right.

So four and nine are square numbers, and they're square because they have the factors, two multiplied by two is equal to four, and three multiplied by three is equal to nine.

So they make those numbers slightly different, and that means that they have an odd number of factors as well, which makes them even more special and interesting.

Okay you may have spotted lots of other things there.

Well done if you did.

So spot any other patterns.

We're going to move on slightly.

What I want to do now is identify the prime numbers all the way through to 50, and it might be that you use a factor bug to help you to be able to sort things, and that's great if you do, being really thorough, but we did just do some stuff on it in the last slide, so you might be able to remember that and that can help us.

Now we said before that one we wouldn't say is a prime number because it's only got just the factor of one.

It's just itself, right, but we know that two is a prime number.

That's our first prime number.

Now we could be clever now because we know that every other even number after two can't be a prime number because it's going to be a multiple of two, and if you count itself and one, then you've got two multiplied by whatever it is, so it's always going to be, we can almost rule out all of this row, sorry all of this column, all of this column, and this one, and this one, and this one.

We can ignore them now because we know that they're not going to be prime numbers.

So next one, we dealt with three.

Okay so three and one only factors, no others.

Yeah, great.

Four we can rule out.

Five is going to be our next prime number.

Six we can rule out.

Seven, yep great, seven is our next prime number.

Now ignoring eight, what about nine? Ah, now we did say about nine that nine was kind of special, because three multiplied by three is equal to nine, and one multiplied by nine is equal to nine.

So we know that nine is not a prime number.

So the next one is 11, and then 13.

Now what about 15? That's right, well done.

So three multiplied by five is equal to 15, and one multiplied by 15.

So we know that 15 can't be a prime number.

17 is our next one, and then following that we've got 23.

We've also got, and I think I might've missed out, now can you find the other remaining prime numbers up to 50? Okay so I want you to find out the remaining prime numbers up to 50.

As a bit of a trick, you may notice this, there might be one up to 23 that I've ignored, that I've missed out.

So bit of a trick there.

Can we find all the remaining prime numbers? And see if you can find the one that I missed out as a bit of a test.

Okay so pause the video now and then we'll come back and show you.

Okay how did we do guys? Brilliant.

Great, so let's have a look at those remaining prime numbers that we should've found.

Okay there they are, all the prime numbers, I think all of them, and most importantly did you spot the one that I had missed out before? Yes, there it is.

So 19 is a prime number, and I tried to fool you with 23.

So hopefully you spotted that.

Great job guys.

So let's move on slightly then.

If I change that around, let's go back a slide.

We've got numbers to 50 up here but now I've changed the structure of my number grids, try and help show you something which I though was really interesting.

So have a look at this.

What do you notice about the patterns of where the prime numbers are? So pause here and have a think.

What can you identify? There's a bit of a hint there to help you.

Okay so what did we identify? Okay great.

Hopefully you've noticed that nearly all prime numbers come either just before or just after a multiple of six.

I think it's really interesting when we see it like this, it identifies something that we weren't able to see in other grids, and that's why it's really important that we look at numbers in lots of different ways with lots of representations to help us to identify patterns, and that's a really interesting pattern to explore a little bit more if you get time.

Now our task today is to go on and try and explore in a bit more detail some of these things.

So I've got a factors and multiples game for us to play, and the aim for us here is to try and make the longest possible chain that you can, where each number is a factor or a multiple of the number before.

Okay you can only use each number once, so you need to make sure you check off numbers as you go.

So to show you an example of how this might work, we might start with the number five.

Now I need to have either a factor or a multiple of five.

Now thinking back, five is a prime number.

So it can't have any other factors unless we're going to go to one, and that might be confusing.

So let's go for a multiple.

Let's go for 50.

Okay so now I need either a factor of 50 or I need a multiple of 50.

So since the only multiple I could think of is 100, let's not go for that.

Let's go for 10.

So now from 10 I'm going to use another factor, and I know that two is a factor of 10.

Now I need a multiple of two 'cause I know that two's a prime number.

Let's go for 88, why not? Look at 88, and then I need a factor or a multiple.

I can't have a multiple really 'cause the next multiple is going to be too high, so we're going to go for 11.

Do you get the idea guys? Okay brilliant.

So it's all about making sure that we get the factors and the multiples and make sure we double check to know it's a factor or the multiple.

Now it might be an interesting thing to do if you've got a hundred grid at home that you can draw on, you might want to check them off to be able to do it.

You may want to do this with a friend and you could almost make it a competition to see who can make the first mistake, or you might want to do it that you have a go and then your friend has a go and see who can get the highest chain or the longest chain.

Okay so lots of different ways that you can explore and play this game, but it's just all about practising factors and multiples and just double checking to know you're right, getting really familiar with it.

Okay guys.

I've played this loads with some of my friends and we love it.

So hopefully you will too.

Okay have lots of fun with that.

Okay you can see I just continued a little bit further so, okay it's time for you to have a go now.

If you want to you can go back to my slide so you can pause it so you can see the structure, but really you just need to get yourself a hundred grid, okay.

So when you're ready, pause the video, and have a go at that, and then just play and we'll finish off the lesson.

Okay that was the end of the lesson today guys.

Remember if you would like, please ask your parent or your carer to share your work on Twitter and make sure you tag us in it to show all of the amazing learning that you've been doing.

It's been great today guys.

I hope you have fun with that, and loads of fun exploring multiples and factors.

Make sure that you do that consolidation and reviewing the learning by doing that end of lesson quiz.

Thanks a lot guys.

I'll see you again soon.

Bye-bye.