National Council for Teachers of Mathematics

Curriculum Standards

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  • In grades 5-8, the mathematics curriculum should include numerous and varied experiences
    with problem solving as a method of inquiry and application so that students can--
  • use problem-solving approaches to investigate and understand mathematical content;
  • formulate problems from situations within and outside mathematics;
  • develop and apply a variety of strategies to solve problems, with emphasis on
  • multistep and nonroutine problems;
  • verify and interpret results with respect to the original problem situation;
  • generalize solutions and strategies to new problem situations;
    acquire confidence in using mathematics meaningfully.

In grades 5-8, the study of mathematics should include opportunities to communicate so that students can--
  • model situations using oral, written, concrete, pictorial, graphical, and algebraic methods;
  • reflect on and clarify their own thinking about mathematical ideas and situations;
  • develop common understandings of mathematical ideas, including the role of definitions;
  • use the skills of reading, listening, and viewing to interpret and evaluate mathematical ideas;
  • discuss mathematical ideas and make conjectures and convincing arguments;
  • appreciate the value of mathematical notation and its role in the development of mathematical ideas.
In grades 5-8, reasoning shall permeate the mathematics curriculum so that students can--
  • recognize and apply deductive and inductive reasoning;
  • understand and apply reasoning processes, with special attention to spatial reasoning and reasoning with
    proportions and graphs;
  • make and evaluate mathematical conjectures and arguments;
  • validate their own thinking;
  • appreciate the pervasive use and power of reasoning as a part of mathematics.
In grades 5-8, the mathematics curriculum should include the investigation of mathematical connections so that
students can--
  • see mathematics as an integrated whole;
  • explore problems and describe results using graphical, numerical, physical, algebraic, and verbal mathematical models or representations;
  • use a mathematical idea to further their understanding of other mathematical ideas;
  • apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as art, music, psychology, science, and business;
  • value the role of mathematics in our culture and society.
In grades 5-8, the mathematics curriculum should include explorations of patterns and functions so that students
  • describe, extend, analyze, and create a wide variety of patterns;
  • describe and represent relationships with tables, graphs, and rules;
  • analyze functional relationships to explain how a change in one quantity results in a change in another;
  • use patterns and functions to represent and solve problems.

In grades 5-8, the mathematics curriculum should include explorations of algebraic concepts and processes so that
students can-
  • understand the concepts of variable, expression, and equation;
  • represent situations and number patterns with tables, graphs, verbal rules, and equations and explore the
    interrelationships of these representations;
  • analyze tables and graphs to identify properties and relationships;
  • develop confidence in solving linear equations using concrete, informal, and formal methods;
  • investigate inequalities and nonlinear equations informally;
  • apply algebraic methods to solve a variety of real-world and mathematical problems.

In grades 5-8, the mathematics curriculum should include the study of the geometry of one, two, and three
dimensions in a variety of situations so that students can--
  • identify, describe, compare, and classify geometric figures;
  • visualize and represent geometric figures with special attention to developing spatial sense;
  • explore transformations of geometric figures;
  • represent and solve problems using geometric models;
  • understand and apply geometric properties and relationships;
  • develop an appreciation of geometry as a means of describing the physical world.
STANDARD 13. MEASUREMENT In grades 5-8, the mathematics curriculum should include extensive concrete experiences using measurement so
that students can--
  • extend their understanding of the process of measurement;
  • estimate, make, and use measurements to describe and compare phenomena;
  • select appropriate units and tools to measure to the degree of accuracy required in a particular situation;
  • understand the structure and use of systems of measurement;
  • extend their understanding of the concepts of perimeter, area, volume, angle measure, capacity, and weight
    and mass;
  • develop the concepts of rates and other derived and indirect measurements;
  • develop formulas and procedures for determining measures to solve problems.