Mathematics Frameworks
STANDARDS -- PATTERNS, RELATIONS AND FUNCTIONS
Patterns and Relationships (NCTM Standard 13)
In grades K-4 the mathematics curriculum 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. | |
STANDARDS -- PATTERNS, RELATIONS AND FUNCTIONS
Patterns and Functions (NCTM Standard 8)
In grades 5-8, the mathematics curriculum 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)
In grades 5-8, the mathematics curriculum 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. | |
Algebra (NCTM Standard 5)
In grades 9-12, the mathematics curriculum 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)
In grades 9-12, the mathematics curriculum 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)
In grades 9-12, the mathematics curriculum 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)
In grades 9-12, the mathematics curriculum 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, RELATIONS AND FUNCTIONS
In the adult basic education classroom, curriculum design 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)
In the adult basic education classroom, curriculum design 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. | |
Go to Standard I Mathematics as Problem Solving
Go to Standard II Mathematics as Communication
Go to Standard III Mathematics as Reasoning
Go to Standard IV Mathematical Connections
Go to Standard V Number and Number System Standards
Go to Standard VI Estimation and Computation
Go to Standard VIII Geometry and Measurement
Go to Standard IX Statistics and Probability
Return to Mathematics Curriculum Frameworks