
District Frameworks  Mathematics
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Standard 7
Patterns, Relations & Functions
Grades K4
Patterns and Relationships (NCTM Standard 13)  shall include the study of patterns and relationships so that students will:
 Recognize, describe, extend, and create a wide variety of patterns;
 Represent and describe mathematical relationships;
 Explore the use of variables and open sentences to express relationships.
Grades 58
Patterns and Functions (NCTM Standard 8)  shall include explorations of patterns and functions so that students will:
 Describe, extend, analyze, and create a wide variety of patterns;
 Describe and represent relationships with tables, graphs, and rules;
 Analyze functional relationships to explain how a change in one quantity results in a change in another;
 Use patterns and functions to represent and solve problems.
Algebra (NCTM Standard 9)  shall include exploration of algebraic concepts and processes so that students will:
 Understand the concepts of variable, expression, and equation;
 Represent situations and number patterns with tables, graphs, verbal rules, and equations and explore the interrelationships of these representations;
 Analyze tables and graphs to identify properties and relationships;
 Develop confidence in solving linear equations using concrete, informal, and formal methods;
 Investigate inequalities and nonlinear equations informally;
 Apply algebraic methods to solve a variety of realworld and mathematical problems.
Grades 912
Algebra (NCTM Standard 5)  shall include the continued study of algebraic concepts and methods so that all students will:
 Represent situations that involve variable quantities with expressions, equations, inequalities, and matrices;
 Use tables and graphs as tools to interpret expressions, equations, and inequalities;
 Operate on expressions and matrices, and solve equations and inequalities;
 Appreciate the power of mathematical abstraction and symbolism;
and, in addition, collegeintending students will:
 Use matrices to solve linear systems;
 Demonstrate technical facility with algebraic transformations, including techniques based on the theory of equations.
Functions (NCTM Standard 6)  shall include the continued study of functions so that all students will:
 Model realworld phenomena with a variety of functions;
 Represent and analyze relationships using tables, verbal rules, equations, and graphs;
 Translate among tabular, symbolic, and graphical representations of functions;
 Recognize that a variety of problem situations can be modeled by the same type of function;
 Analyze the effects of parameter changes on the graphs of functions;
and, in addition, collegeintending students will:
 Understand operations on, and the general properties and behavior of, classes of functions.
Trigonometry (NCTM Standard 9)  shall include the study of trigonometry so that all students will:
 Apply trigonometry to problem situations involving triangles;
 Explore periodic realworld phenomena using the sine and cosine functions;
and, in addition, collegeintending students will:
 Understand the connections between trigonometric and circular functions;
 Use circular functions to model periodic realworld phenomena;
 Apply general graphing techniques to trigonometric functions;
 Solve trigonometric equations and verify trigonometric identities;
 Understand the connections between trigonometric functions and polar coordinates, complex numbers, and series.
Conceptual Underpinnings of Calculus (NCTM Standard 13)  shall include the informal exploration of calculus concepts from both a graphical and a numerical perspective so that all students will:
 Determine maximum and minimum points of a graph and interpret the results in problem situations;
 Investigate limiting processes by examining infinite sequences and series and areas under curves;
and, in addition, collegeintending students will:
 Understand the conceptual foundations of limit, the area under a curve, the rate of change, and the slope of a tangent line, and their applications in other disciplines;
 Analyze the graphs of polynomial, rational, radical, and transcendental functions.
ADULT BASIC EDUCATION
Patterns, Relationships, and Functions (ABE Standard 7)  shall include approaches to teaching about patterns, relationships, and functions which allow the learner to:
 Explore, recognize, analyze, and extend patterns in mathematical and realworld situations;
 Articulate and represent number and data relationships using words, tables, graphs, and rules;
 Discover and use patterns and functions to represent and solve problems.
Algebra (ABE Standard 8)  shall include approaches to teaching algebra which allow the learner to:
 Represent arithmetic patterns and realworld situations using tables, graphs, verbal rules, equations, and explore the interrelationships of these presentations;
 Understand the concepts of and recognize the use of variables, expressions and equations;
 Develop confidence in solving equations in one or two variables using concrete, informal, and formal methods;
 Apply algebraic methods to solve and represent a variety of testrelated, workspecific or realworld mathematical problems.
