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See: Math

Joe,

I very much like your idea of using spreadsheets to model different "savings and loan" arrangements.

I think that playing around with numbers is essential to building intuition. And spreadsheets seem like an excellent way to do that, especially for that kind of problem. And a very natural one that leads directly into work skills.

I think a key thing to learn is the different kinds of families of functions and their qualitative differences, such as linear vs. exponential.

If math is a study of systems, then that includes especially realizing when systems or models break down, when they apply and when they don't apply.

Among my favorite exponential modeling problems are:

• Given the current population and current growth rate work backwards to figure out when the first person appeared ("Adam"), the second person ("Eve") and so on.
• Native Americans in Manhattan (NY) are said to have sold the island for $24 in 1624. Supposing they invested that wisely (model different rates), what would their investment be worth today? Could they buy Manhattan back?
• There is an old classic story about the inventors of checkers and chess in India. The king offered them to name a gift they would like to receive for each of 64 days, corresponding to the squares on the board. The inventor of checkers wanted 1,000 gold coins per day. The inventor of chess wanted one grain of rice on the first day, but the amount doubled every following day. How much rice would that be on the last day?

Andrius