You know what fact families are? In elementary and middle school, this is increasingly common terminology to express relationships among basic number facts. A sample fact family:

Fact family thinking is intended to encourage connections between operations and their inverses. Addition and subtraction fact families work the same way as multiplication and division fact families:

I have written a lot about logarithms this past year and I keep wondering about ways to get students’ minds wrapped around the relationships that logarithms are intended to express, and to focus less on the notation.

Here is a fact family for an exponential relationship.

Some things I notice:

- We’re not used to thinking about roots, logs and exponentials all at the same time. Maybe we should be.
- Exponentiation is not commutative, so we only have three facts in the family, not four. That seems useful to know.
- Off the top of my head, I can’t think of another non-commutative binary operation (besides those listed out above), so I can’t test the proposition that:
- All non-commutative binary operations will necessarily have TWO inverse operations in their fact families.