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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. 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.