Mathematics Curriculum Framework
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|
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.