Starting with 15 coins. Move the coins into any amount of piles of any size. Now, each move consists of taking one coin from each pile and creating a new pile with these coins. Continue to do this until you have a set of piles which has already occurred.
Questions to Consider
How many steps does it take for the game to end?
How do you know the game will eventually end?
What happens if you start with a different number of coins?
Will you always get a pattern that will repeat at each step?
If not, how many steps can it take for your pattern to repeat?
This activity works well with young and older students alike.
For younger students (5 years olds) start them with 5 coins.
For older students 15 or 21.