In grades 9-12, the mathematics curriculum should include the continued study of algebraic concepts and methods so that students can:

- Represent situations that involve variable quantities with expressions, equations, inequalities, and matrices
- Use tables and graphs as tools to interpret expressions, equations, and inequalities
- Operate on expressions and matrices, and solve equations and inequalities
- Appreciate the power of mathematical abstraction and symbolism

*Benchmarks* 11C (Common Themes: Constancy and Change)

Grades 6-8, page 274

Symbolic equations can be used to summarize how the quantity of something
changes over time or in response to other changes.

*Benchmarks* 4F (The Physical Setting: Motion)

Grades 9-12, page 91

The change in motion of an object is proportional to the applied force
and inversely proportional to the mass.

*Benchmarks* 4G (The Physical Setting: Forces of Nature)

Grades 9-12, page 96

Gravitational force is an attraction between masses. The strength of
the force is proportional to the masses and weakens rapidly with increasing
distance between them.

*Benchmarks* 12B (Habits of Mind: Computation and Estimation)

Grades 9-12, page 291

Use ratios and proportions, including constant rates, in appropriate
problems.

*Benchmarks* 11C (Common Themes: Constancy and Change)

Grades 9-12, page 275

Graphs and equations are useful (and often equivalent) ways for depicting
and analyzing patterns of change.

*Benchmarks* 9B (The Mathematical World: Symbolic Relationships)

Grades 9-12, page 220

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.

*Benchmarks* 9B (The Mathematical World: Symbolic Relationships)

Grades 9-12, page 220

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. Symbolic statements can be combined to
look for values of variables that will satisfy all of them at the same
time.

*Benchmarks* 9B (The Mathematical World: Symbolic Relationships)

Grades 9-12, page 221

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 more than one, and sometimes maybe not at all.

*Benchmarks* 12B (The Mathematical World: Symbolic Relationships)

Grades 9-12, page 291

Find answers to problems by substituting numerical values in simple
algebraic formulas and judge whether the answer is reasonable by reviewing
the process and checking against typical values.

*Benchmarks* 2C (The Nature of Mathematics: Mathematical Inquiry)

Grades 9-12, page 38

Some work in mathematics is much like a game mathematicians choose
an interesting set of rules and then play according to those rules to see
what can happen. The more interesting the results, the better. The only
limit on the set of rules is that they should not contradict one another.