Foundations

Variables can be used to build rules that represent functions. Equivalence means that an expression will produce the same output for every possible input, which can be seen in tables, graphs, and rules.

Equations can be written to solve specific questions about real-life situations. Solutions to equations are values that make the equation true, and those solutions can be found using reasoning/guess-and-check, tables, graphs, technology, or algebraic manipulation.

Functions can be represented in multiple ways, including algebraic (symbolic), graphical, verbal, and tabular representations. Links among these representations are important to studying relationships and change.

Ideas and results in geometry can often be useful in modeling real life situations and in finding solutions to real life problems. This usually involves simplifying the problem in to a "pure" geometry problem and then interpreting the results in the original context.