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.

• 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 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.

• Analyze change in various contexts.
  In grades 6-8 all students should use graphs to analyze the nature of changes in quantities in linear relationships.

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.