Mathematics Curriculum Framework
November 2000

Learning Standards

Patterns, Relations, and Algebra
for Grades 9-10

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:
10.P.1Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative, recursive (e.g., Fibonacci Numbers), linear, quadratic, and exponential functional relationships.
10.P.2Demonstrate an understanding of the relationship between various representations of a line. Determine a line's slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a geometric description of the line, e.g., by using the "point-slope" or "slope y-intercept" formulas. Explain the significance of a positive, negative, zero, or undefined slope.
10.P.3Add, subtract, and multiply polynomials. Divide polynomials by monomials.
10.P.4Demonstrate facility in symbolic manipulation of polynomial and rational expressions by rearranging and collecting terms; factoring (e.g., a2 - b2 = (a + b)(a - b), x2 + 10x + 21 = (x + 3)(x + 7), 5x4 + 10x3 - 5x2 = 5x2 (x2 + 2x - 1)); identifying and canceling common factors in rational expressions; and applying the properties of positive integer exponents.
10.P.5Find solutions to quadratic equations (with real roots) by factoring, completing the square, or using the quadratic formula. Demonstrate an understanding of the equivalence of the methods.
10.P.6Solve equations and inequalities including those involving absolute value of linear expressions (e.g., |x - 2| > 5) and apply to the solution of problems.
10.P.7Solve everyday problems that can be modeled using linear, reciprocal, quadratic, or exponential functions. Apply appropriate tabular, graphical, or symbolic methods to the solution. Include compound interest, and direct and inverse variation problems. Use technology when appropriate.
10.P.8Solve everyday problems that can be modeled using systems of linear equations or inequalities. Apply algebraic and graphical methods to the solution. Use technology when appropriate. Include mixture, rate, and work problems.

Exploratory Concepts and Skills
for Grades 9-10 and Single-Subject Courses

  • Explore matrices and their operations. Use matrices to solve systems of linear equations.
  • Investigate recursive function notation.
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