Follow some numbers and see where they go.
The simple rule is: choose a number, add the digits together then multiply by 2 and then do the same again.
Suppose you start with 56 then you get 5+6 = 11 and 11 x 2 =22 so the next number is 22. Carry on and you get: 56, 22, 8, 16, 14, 10, 2, 4, 8, 16, 14, 10, 2, …
What happens when you start with different numbers?
What happens when you try different rules like add the digits and multiply by 3? You might like to use an arrow diagram like this and add more branches to it:
Can you explain why you get repeating patterns every time?
Thank you to NRICH for this activity.