So many of us are using mobile phones and you have numbers like that one above. (+44 instead of the first 0 when you are phoning the UK from abroad.)

Some numbers are easy to remember!

Some seem to have a pattern about them!

Let's have a look at how we might invent some mobile phone numbers that would be easy to remember.

We could start with a number and have a simple rule that gives us the next number, like starting with 3 and adding 2 each time:

1 3 5 7 etc.

and when the number is bigger than 9 we could just write down the units figure. For example:

1 3 5 7 9 1 3 5 7 9 1 3

Here are some suggestions about how you could go on with this idea:
but we could start with any of the numbers, 1 ... 9.

A. Try adding on 2 each time as in the example above, but starting with any number, 1 ... 9 and see what you get.

Try adding on 3 each time instead - starting with 1 then 2 then 3 ...
(For example starting with 5 it would be 5 8 1 4 7 0 3 6 9 2 5 8.)

B. We could try adding on a 4 each time, and so on.

C. We could multiply instead. Suppose we've done multiplying by 2, 3, 4 and 5 and we come to 6. Starting with
1 we'd have:1 6 6 6 6 6 6 6 6 6 6 6
2 we'd have: 2 2 2 2 2 2 2 2 2 2 2 2
3 we'd have: 3 8 8 8 8 8 8 8 8 8 8 8

So carry on!
Again, what do you notice? Have a chat to someone else about it.

D. We could use two rules, but only changing one at a time - I'll show you what I mean. Suppose we use "add ... then multiply by 9" and have "adding 1" as a first idea.
Starting with
1 we'd have : 1 8 1 8 1 8 1 8 1 8 1 8
2 we'd have : 2 7 2 7 2 7 2 7 2 7 2 7
3 we'd have : 3 6 3 6 3 6 3 6 3 6 3 6

... so carry on.

But we could add 2 or 3 or 4 ... each time instead and explore the nine patterns each time.
So, for example, adding on 5 then multiplying by 9 we get the following 9 patterns

1 4 1 4 1 4 1 4 1 4 1 4

2 3 2 3 2 3 2 3 2 3 2 3

3 2 3 2 3 2 3 2 3 2 3 2

4 1 4 1 4 1 4 1 4 1 4 1

5 0 5 0 5 0 5 0 5 0 5 0

6 9 6 9 6 9 6 9 6 9 6 9

7 8 7 8 7 8 7 8 7 8 7 8

8 7 8 7 8 7 8 7 8 7 8 7

9 6 9 6 9 6 9 6 9 6 9 6

E. You may be getting the idea. You could use any combination of rules.