A) Extend the properties of exponents to rational exponents.

B) Use properties of rational and irrational numbers.

C) Reason quantitatively and use units to solve problems.

D) Interpret the structure of expressions.

E) Write expressions in equivalent forms to solve problems.

F) Perform arithmetic operations on polynomials.

G) Create equations that describe numbers or relationships.

H) Understand solving equations as a process of reasoning and explain the reasoning.

I) Solve equations and inequalities in one variable.

J) Represent and solve equations and inequalities graphically.

K) Understand the concept of a function and use function rotation.

L) Interpret functions that arise in applications in terms of a context.

M) Analyze functions using different representations.

N) Build a function that models a relationship between two quantities.

O) Prove geometric theorems.

P) Summarize, represent, and interpret data on a single count or measurement variable.

A) Apply mathematics to solve well-posed problems arising in everyday life, society, and the workplace.

B) Select and use appropriate tools strategically.

C) Interpret results in the context of a situation.

D) Identify important quantities in a practical situation and map their relationships (e.g., using diagrams, two-way tables, graphs, flow charts, or formulas).

A) Test propositions or conjectures with specific examples.

B) Construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures.

C) State logical assumptions being used.

D) Use the technique of breaking an argument into cases.

E) Distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in the argument-explain what it is.

F) Base arguments on concrete referents such as objects, drawings, diagrams, and actions.

G) At later grades, determine conditions under which an argument does and does not apply. (For example, area increases with perimeter for squares, but not for all plan figures.)

A) Apply mathematics to solve problems arising in everyday life, society, and the workplace.

B) Construct, autonomously, chains of reasoning to justify mathematical models used, interpretations made, and solutions proposed for a complex problem.

C) State logical assumptions being used.

D) Interpret results in the context of a situation.

E) Analyze the adequacy of and make improvements to an existing model or develop a mathematical model of a real phenomenon.

F) Identify important quantities in a practical situation and map their relationships (e.g., using diagrams, two-way tables, graphs, flow charts, or formulas).

G) Identify, analyze, and synthesize relevant external resources to pose or solve problems.