### Standard 5: Algebra

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
• Benchmarks 11C (Common Themes: Constancy and Change)
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)
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)
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.

• Use tables and graphs as tools to interpret expressions, equations, and inequalities
• Benchmarks 12B (Habits of Mind: Computation and Estimation)
Use ratios and proportions, including constant rates, in appropriate problems.

Benchmarks 11C (Common Themes: Constancy and Change)
Graphs and equations are useful (and often equivalent) ways for depicting and analyzing patterns of change.

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

• Operate on expressions and matrices, and solve equations and inequalities
• Benchmarks 9B (The Mathematical World: Symbolic Relationships)
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)
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)
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.

• Appreciate the power of mathematical abstraction and symbolism
• Benchmarks 2C (The Nature of Mathematics: Mathematical Inquiry)