The answers in the comments are probably the best (in particular @James S. Cook's advice to talk to a professor at a local university if you have such a connection) but here's at least a list to get you started: Given that you've got quite a range of interested there I would suggest going through the MAA's list of Math programs:
Start with two equations that are the same in every way, like this:
2 + 2 = 4 and 2 + 2 = 4
Now, add "4" more to each of the two equations, one at a time, so you'll get 8 in each equation. But do it different ways in each of the two equations.
1.) Add all of the "4" more to the second "2" in the first equation: 2 + 6 = 8 (and 2 + 2 = 4)
2.) Now split up ...