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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.