A. Patterns

1. Recognize, describe, extend, and create patterns involving whole numbers, rational numbers, and integers.
   • Descriptions using tables, verbal and symbolic rules, graphs, simple equations or expressions
   • Finite and infinite sequences
   • Arithmetic sequences (i.e., sequences generated by repeated addition of a fixed number, positive or negative)
   • Geometric sequences (i.e., sequences generated by repeated multiplication by a fixed positive ratio, greater than 1 or less than 1)
   • Generating sequences by using calculators to repeatedly apply a formula

B. Functions and Relationships

1. Graph functions, and understand and describe their general behavior.
   • Equations involving two variables
   • Rates of change (informal notion of slope)
2. Recognize and describe the difference between linear and exponential growth, using tables, graphs, and equations.

C. Modeling

1. Analyze functional relationships to explain how a change in one quantity can result in a change in another, using pictures, graphs, charts, and equations.
2. Use patterns, relations, symbolic algebra, and linear functions to model situations.
   • Using concrete materials (manipulatives), tables, graphs, verbal rules, algebraic expressions/equations/inequalities
   • Growth situations, such as population growth and compound interest, using recursive (e.g., NOW-NEXT) formulas (cf. science standard 5.5 and social studies standard 6.6)

D. Procedures

1. Use graphing techniques on a number line.
   • Absolute value
   • Arithmetic operations represented by vectors (arrows) (e.g., "-3 + 6" is "left 3, right 6")
2. Solve simple linear equations informally, graphically, and using formal algebraic methods.
   • Multi-step, integer coefficients only (although answers may not be integers)
   • Using paper-and-pencil, calculators, graphing calculators, spreadsheets, and other technology
3. Solve simple linear inequalities.
4. Create, evaluate, and simplify algebraic expressions involving variables.
   • Order of operations, including appropriate use of parentheses
   • Distributive property
   • Substitution of a number for a variable
   • Translation of a verbal phrase or sentence into an algebraic expression, equation, or inequality, and vice versa
5. Understand and apply the properties of operations, numbers, equations, and inequalities.
   • Additive inverse
   • Multiplicative inverse
   • Addition and multiplication properties of equality
   • Addition and multiplication properties of inequalities