A. Patterns

1. Recognize, describe, extend, and create patterns involving whole numbers and rational numbers.
   • Descriptions using tables, verbal rules, simple equations, and graphs
   • Formal iterative formulas (e.g., NEXT = NOW * 3)
   • Recursive patterns, including Pascal's Triangle (where each entry is the sum of the entries above it) and the Fibonacci Sequence: 1, 1, 2, 3, 5, 8, . . . (where NEXT = NOW + PREVIOUS)

B. Functions and Relationships

1. Describe the general behavior of functions given by formulas or verbal rules (e.g., graph to determine whether increasing or decreasing, linear or not).

C. Modeling

1. Use patterns, relations, and linear functions to model situations.
   • Using variables to represent unknown quantities
   • Using concrete materials, tables, graphs, verbal rules, algebraic expressions/equations/inequalities
2. Draw freehand sketches of graphs that model real phenomena and use such graphs to predict and interpret events.
   • Changes over time
   • Relations between quantities
   • Rates of change (e.g., when is plant growing slowly/rapidly, when is temperature dropping most rapidly/slowly)

D. Procedures

1. Solve simple linear equations with manipulatives and informally.
   • Whole-number coefficients only, answers also whole numbers
   • Variables on one or both sides of equation
2. Understand and apply the properties of operations and numbers.
   • Distributive property
   • The product of a number and its reciprocal is 1
3. Evaluate numerical expressions.
4. Extend understanding and use of inequality.
   • Symbols ( ³ , ¹ , £ )