In some cases the more of something there is, the more rapidly it may change (as the number of births is proportional to the size of the population).
Learning Goal 1b
Sometimes the rate of change of something depends on how much there is of something else (as the rate of change of speed is proportional to the amount of force acting).
Learning Goal 2a
Symbolic statements can be manipulated by rules of mathematical logic to produce other statements of the same relationship, which may show some interesting aspect more clearly.
Learning Goal 2b
Symbolic statements can be combined to look for values of variables that will satisfy all of them at the same time.
Learning Goal 3
Any mathematical model, graphic or algebraic, is limited in how well it can represent how the world works. The usefulness of a mathematical model for predicting may be limited by uncertainties in measurements, by neglect of some important influences, or by requiring too much computation.
Learning Goal 4
Tables, graphs, and symbols are alternative ways of representing data and relationships that can be translated from one to another.
Learning Goal 5
When a relationship is represented in symbols, numbers can be substituted for all but one of the symbols and the possible value of the remaining symbol computed. Sometimes the relationship may be satisfied by one value, sometimes by more than one, and sometimes not at all.