Mathematics Curriculum Framework
November 2000

## Learning Standards by Strand

### Patterns, Relations, and Algebra for Grades 7-8

 Understand patterns, relations, and functions Represent and analyze mathematical situations and structures using algebraic symbols Use mathematical models to represent and understand quantitative relationships Analyze change in various contexts

#### Learning Standards

Students engage in problem solving, communicating, reasoning, connecting, and representing as they:
 8.P.1 Extend, 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.2 Evaluate simple algebraic expressions for given variable values, e.g., 3a2 - b for a = 3 and b = 7. 8.P.3 Demonstrate an understanding of the identity (-x)(-y) = xy. Use this identity to simplify algebraic expressions, e.g., (-2)(-x+2) = 2x - 4. 8.P.4 Create and use symbolic expressions and relate them to verbal, tabular, and graphical representations. 8.P.5 Identify 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.6 Identify 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.7 Set up and solve linear equations and inequalities with one or two variables, using algebraic methods, models, and/or graphs. 8.P.8 Explain 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.9 Use linear equations to model and analyze problems involving proportional relationships. Use technology as appropriate. 8.P.10 Use 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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