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NCTM Standards


NCTM Standards 2000 addressed within the InterMath Fractions and Decimals Unit

Grades 6-8



NUMBER and OPERATIONS STANDARD

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

  • Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
    In grades 6-8 all students should develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation; use factors, multiples, prime factorization, and relatively prime numbers to solve problems; and develop meaning for integers and represent and compare quantities with them.
  • Understand meanings of operations and how they relate to one another.
    In grades 6-8 all students should understand the meaning and effects of arithmetic operations with fractions, decimals, and integers; and use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals.
  • Compute fluently and make reasonable estimates.
    In grades 6-8 all students should develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use.


ALGEBRA STANDARD

Instructional programs from prekindergarten 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 develop an initial conceptual understanding of different uses of variables.
  • 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 prekindergarten 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 prekindergarten 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 prekindergarten 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 prekindergarten 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 prekindergarten 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.