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National
Council for Teachers of Mathematics
Curriculum
Standards
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STANDARD
1. MATHEMATICS AS PROBLEM SOLVING
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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.
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STANDARD
2. MATHEMATICS AS COMMUNICATION
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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.
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STANDARD
3. MATHEMATICS AS REASONING
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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.
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STANDARD
4. MATHEMATICAL CONNECTIONS
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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.
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STANDARD
8. PATTERNS AND FUNCTIONS
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In grades
5-8, 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.
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STANDARD
9. ALGEBRA
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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.
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STANDARD
12. GEOMETRY
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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.
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| 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.
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