Mathematics Curriculum Framework
November 2000

Learning Standards by Strand

Patterns, Relations, and Algebra
for Grades 7-8

cross symbolUnderstand patterns, relations, and functions
solid circle symbolRepresent and analyze mathematical situations and structures using algebraic symbols
solid triangle symbolUse mathematical models to represent and understand quantitative relationships
solid square symbolAnalyze change in various contexts

Learning Standards

Students engage in problem solving, communicating, reasoning, connecting, and representing as they:
8.P.1Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic expressions. Include arithmetic and geometric progressions, e.g., compounding.
8.P.2Evaluate simple algebraic expressions for given variable values, e.g., 3a2 - b for a = 3 and b = 7.
8.P.3Demonstrate an understanding of the identity (-x)(-y) = xy. Use this identity to simplify algebraic expressions, e.g., (-2)(-x+2) = 2x - 4.
8.P.4Create and use symbolic expressions and relate them to verbal, tabular, and graphical representations.
8.P.5Identify the slope of a line as a measure of its steepness and as a constant rate of change from its table of values, equation, or graph. Apply the concept of slope to the solution of problems.
8.P.6Identify the roles of variables within an equation, e.g., y = mx + b, expressing y as a function of x with parameters m and b.
8.P.7Set up and solve linear equations and inequalities with one or two variables, using algebraic methods, models, and/or graphs.
8.P.8Explain and analyze-both quantitatively and qualitatively, using pictures, graphs, charts, or equations-how a change in one variable results in a change in another variable in functional relationships, e.g., C = ?d, A = ?r2 (A as a function of r), Arectangle = lw (Arectangle as a function of l and w).
8.P.9Use linear equations to model and analyze problems involving proportional relationships. Use technology as appropriate.
8.P.10Use tables and graphs to represent and compare linear growth patterns. In particular, compare rates of change and x- and y-intercepts of different linear patterns.

Exploratory Concepts and Skill
for Grades 7-8 and Single-Subject Courses

  • Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative and recursive (e.g., Pascal's triangle), and linear functional relationships.
  • Use tables, graphs, and appropriate technology to explore quadratic and exponential growth patterns.
  • Investigate the use of systems of equations, tables, and graphs to represent mathematical relationships.
  • Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations.
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