Wachusett Regional School District
Wachusett Mountain

District Frameworks - Mathematics

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Standard 7

Patterns, Relations & Functions

Grades K-4

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 5-8

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 real-world and mathematical problems.

Grades 9-12

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, college-intending 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 real-world 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, college-intending 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 real-world phenomena using the sine and cosine functions;

and, in addition, college-intending students will:

  • Understand the connections between trigonometric and circular functions; 
  • Use circular functions to model periodic real-world 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, college-intending 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 real-world 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 real-world 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 test-related, work-specific or real-world mathematical problems.