
National
Council for Teachers of Mathematics
Curriculum
Standards
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STANDARD
1. MATHEMATICS AS PROBLEM SOLVING

 In grades 58, the
mathematics curriculum should include numerous and varied experiences
with problem solving as a method of inquiry and application
so that students can
 use problemsolving
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.

STANDARD
2. MATHEMATICS AS COMMUNICATION

In grades
58, 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.

STANDARD
3. MATHEMATICS AS REASONING

In grades
58, 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.

STANDARD
4. MATHEMATICAL CONNECTIONS

In grades 58, 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.

STANDARD
8. PATTERNS AND FUNCTIONS

In grades
58, the mathematics curriculum should include explorations of patterns
and functions so that students
can
 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.

STANDARD
9. ALGEBRA

In grades
58, 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 realworld and mathematical problems.

STANDARD
12. GEOMETRY

In grades
58, 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 58, 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.

