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NCTM Standards


NCTM Standards 2000 Addressed Within the InterMath Patterns Unit:

Grades 6-8


ALGEBRA STANDARD

Instructional programs from pre-kindergarten through grade 12 should enable all students to--

  • Understand patterns, relations, and functions.
    In grades 6-8 all students should represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules; identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations.
  • Represent and analyze mathematical situations and structures using algebraic symbols.
    In grades 6-8 all students should explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope; use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships; recognize and generate equivalent forms for simple algebraic expressions and solve linear equations.
  • Use mathematical models to represent and understand quantitative relationships.
    In grades 6-8 all students should model and solve contextualized problems using various representations, such as graphs, tables, and equations.

PROBLEM SOLVING STANDARD

Instructional programs from pre-kindergarten through grade 12 should enable all students to--

  • build new mathematical knowledge through problem solving;
  • solve problems that arise in mathematics and in other contexts;
  • apply and adapt a variety of appropriate strategies to solve problems;
  • monitor and reflect on the process of mathematical problem solving.

REASONING AND PROOF STANDARD

Instructional programs from pre-kindergarten through grade 12 should enable all students to--

  • recognize reasoning and proof as fundamental aspects of mathematics;
  • make and investigate mathematical conjectures;
  • develop and evaluate mathematical arguments and proofs;
  • select and use various types of reasoning and methods of proof.

COMMUNICATION STANDARD

Instructional programs from pre-kindergarten through grade 12 should enable all students to--

  • organize and consolidate their mathematical thinking through communication;
  • communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
  • analyze and evaluate the mathematical thinking and strategies of others;
  • use the language of mathematics to express mathematical ideas precisely.

CONNECTIONS STANDARD

Instructional programs from pre-kindergarten through grade 12 should enable all students to--

  • recognize and use connections among mathematical ideas;
  • understand how mathematical ideas interconnect and build on one another to produce a coherent whole;
  • recognize and apply mathematics in contexts outside of mathematics.

REPRESENTATION STANDARD

Instructional programs from pre-kindergarten through grade 12 should enable all students to--

  • create and use representations to organize, record, and communicate mathematical ideas;
  • select, apply, and translate among mathematical representations to solve problems;
  • use representations to model and interpret physical, social, and mathematical phenomena.