June 1, 2009

An introduction into linear patterns

- Mathematics > General
- Mathematics > Algebra
- Mathematics > Data Analysis & Probability
- Mathematics > Patterns

- Grade 6
- Grade 7
- Grade 8
- Grade 9
- Grade 10

Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable expressions.

Generalize patterns by describing in words how to find the next term.

Recognize and explain when numerical patterns are linear or nonlinear progressions; e.g., 1, 3, 5, 7... is linear and 1, 3, 4, 8, 16... is nonlinear.

Create visual representations of equation-solving processes that model the use of inverse operations.

Represent linear equations by plotting points in the coordinate plane.

Represent inequalities on a number line or a coordinate plane.

Justify that two forms of an algebraic expression are equivalent, and recognize when an expression is simplified; e.g., 4m = m + m + m + m or a * 5 + 4 = 5a + 4.

Use formulas in problem-solving situations.

Recognize a variety of uses for variables; e.g., placeholder for an unknown quantity in an equation, generalization for a pattern, formula.

Analyze linear and simple nonlinear relationships to explain how a change in one variable results in the change of another.

Use graphing calculators or computers to analyze change; e.g., distance-time relationships.