# Lesson video

In progress...

Hi there, my name is Miss Darwish.

And for your maths lesson today, we are going to be exploring properties of number.

But before we get started, if I could just ask you to take yourself away from any distractions, so you're ready for the lesson.

Okay, so for this lesson, we're going to start off by looking at the number nine, and then we look at multiples of nine and then there'll be a bit of magic maths in there.

And at the end of the session, as always, there will be a quiz for you to complete on today's learning.

So let's get started.

So if I could just ask you to grab yourself a pencil or pen a sheets of paper or a notepad and a ruler so that we can start and begin the lesson.

Okay, first of all, what do you know about multiples of nine? What do you know about the number nine? And then multiples of nine? Tell me some multiples of nine.

Go, shout them to me.

Okay, what do you know about multiples of nine? How do you know if a number is a multiple of nine? Okay.

I'm going to shout some numbers to you, and I want you to give me a thumbs up or say yes, if it's a multiple of nine or a thumbs down or a no, if it's not a multiple of nine, you are ready? Okay, I'll start with some easy ones.

27.

Good.

36.

801.

shshh! 72.

7,281.

Okay, let's have a look.

So, here are some multiples of nine.

So we've got 18, 27, 162 81, 324, 927.

And why are they multiples of nine? Or how do we know, they are multiples of nine? So, we're going to look at the sum of the digits.

So 18, one add eight is equal to nine.

What about 27? Two add seven is equal to nine, well done.

What's the digit sum? Nine.

We've got the nine and then seven add two also make nine.

So we've got two groups of nine or 18 and these are all multiples of nine.

When you add the digits, if they add up to nine or 18 or 27, then it's a multiple of nine, okay? So when I said.

What big numbers did I say? 8,001.

You know that eight add one is nine, okay? Or, can you count all of your own larger numbers that are multiple of nine? I could say 621.

540, five add four is nine.

Okay.

So let's do some magic maths.

I'm going to show you some magic tricks now, okay? Are you ready? So, I have chosen six digits and made a six digit number.

Now, just to be clear, these six digits are random I literally picked any six digits, okay? Three, two, five, six, one five, okay? You can pick any six digits for this.

So, I'm going to want you to do the same soon, but not yet, okay? So just watch.

So I have picked six digits uncompletely random, okay? So you can repeat a digit, like I've repeated the digit five.

Well, you don't have to repeat a digit.

So, three, two, five, six, one, five is now my number.

So I've chosen these digits and I've put them together and now I've made myself a six digit number.

Okay, can you read that six digit number out for me that I've made? 325,615.

Good.

Okay.

So 325,615 is my number now.

Using the same digits, I've created a different number.

I haven't added any new digit in, I haven't taken any digits out.

I made my number and then all I did, was shift the digits around just to make a new number, okay? I'm not adding any other digit 'cause just the ones I've got, I've shifted them around to make a new number.

What's my new number? Can you read it out to me? Let's read it together.

253,165.

Okay, so that's my new number.

Now, my first number, was 325,615.

And my second number just by shifting the digits remember haven't added anything I haven't taken anything away, haven't added any new digits.

It could have, it could have been something different, okay? There was lots of options I could have chose.

This just happened to be what I chose.

And when I subtract them, the difference between both numbers is what? 72,450, okay? What do you notice about the number, 72,450? Is it a multiple of nine? How do you know? Seven add two is equal to nine and four add five is equal to nine.

Wow! It is, in the nine times tables.

72,450 is a multiple of nine.

Now, let's have a think.

You're going to have a go now, okay? So get that pencil or pen and piece of paper ready.

So is this always, sometimes or never true? You're going to do an investigation for me.

Take any number and switch around the digits to create a new number.

The difference will always be a multiple of nine.

Now, I chose a six digit number.

I'm not asking you to choose a six digit number.

It could be a three digit number, a two digit number, a seven digit number, a nine digit number.

Feel free to choose whatever you want, okay? And I want you to have a look, so you going to choose a number and then you're going to switch the digits around to make a different number, and then you're going to subtract them, okay? Do you want to have a go or should we do an example first? Have a go, write down a number.

Finished? Okay.

Now I want you to move the digits around and create another number and subtract them.

Okay, what was your difference between both numbers? Is it in multiple of nine? Yes or no? Okay, let's see.

Let's have a look at another example.

So the more examples we collect, the better it is for us to say, if this is always, sometimes or never true.

So I've got my example, I've got your example and then we've got this other second example.

This is my second example as well.

And if you wanted to do a second example, you can do as well.

So, 8,637, I'm going to move the digits around and create a new number.

I'm going to make, 3,768.

There was lots of different options I could have done.

I could have done 6,837 anyway, I've taken them away and my answer is 4,869.

Is that a multiple of nine? What's four add eight? 12.

That is a multiple of nine.

So our answer is a multiple of nine.

So my two examples prove that actually take any digit, any number sorry, with any digits and then create another number but move and shift digits around, subtract them and the answer seems to be a multiple of nine, or actually so far, this has always been true.

I don't know about you, do you want to have a go at a second example now? And tell me what you think, if this is always or sometimes true? Pick a number, remember any digits, five digit number, four digit number, three digit number.

Obviously it can't be a one digit number And then find the difference and then see what the digit sum is.

Okay.

Let's have a look at some more examples.

So there's the number 42.

Obviously it can only be one other option if I switched the digits, it becomes 24, 42 take away 24 is equal to 18.

It is, it is in the nine times tables.

Interesting is a multiple of nine.

What examples did you get? What did you find? Interesting.

The answer seems to always actually be a multiple of nine.

I'd love to know what you found out.

Okay, now it's time for you to pause the video, have you got the independent task.

Once you've had to go, come back and we'll have a discussion about what you found.

Okay, welcome back.

How did you find that? Hopefully not too tricky? So, independent task.

You had to try and spot and find out which of the numbers was not a multiple of nine.

So let's have a look at 4,518, four add five is nine, eight add one is nine.

It is a multiple of nine.

Second one, 7,325, seven add three, is 10, 10 add five is 15, add two is 17, do think is that one 7,325 is not a multiple of nine? What about the third one? 8,136, eight add one is equal to nine, six add three also equal to nine.

So that second one is not a multiple of nine.

Okay.

And then the next one, 65,331, six add five is 11, 11 add three 14, add four 18, 18 is a multiple of nine, the second one 98,119, it's not, is it? And then 43,317, what's the digit sum? four add three, add three is 10, seven add one is eight, 18.

Okay, and then the last three set of numbers, 784,123, what's the digit sum? 25, it's not, is it? So it's not that first one, 319,608, it is a multiple.

And the last one, 109,845, that one's okay as well.

Okay, do you want to give that a mark and tick at the ones you got right? Okay, well done.

If you'd like to share your work with us here, it's Oak National.