NCTM Mathematics Curriculum Standards for Grades 5-8
 Standard 1  Mathematics as Problem Solving Standard 3  Mathematics as Reasoning Standard 7  Computation and Estimation Standard 8  Patterns and Functions Standard 10 Statistics Standard 13 Measurement

Standard 1: Mathematics as Problem Solving

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:

1) use problem-solving approaches to investigate and understand mathematical content;
2) formulate problems from situations within and outside mathematics;
3) develop and apply a variety of strategies to solve problems, with emphasis on multistep and nonroutine problems;
4) verify and interpret results with respect to new problem situations;
5) acquire confidence in using mathematics meaningfully. .

Standard 3: Mathematics as Reasoning

In grades 5-8, reasoning shall permeate the mathematics curriculum so that students can:

1) recognize and apply deductive and inductive reasoning;
2) understand and apply reasoning processes, with special attention to spatial reasoning and reasoning with proportions and graphs;
3) make and evaluate mathematical conjectures and arguments;
4) validate their own thinking;
5) appreciate the pervasive use and power of reasoning as a part of mathematics.

Standard 7: Computation and Estimation

In grades 5-8, the mathematics curriculum should develop the concepts underlying computation and estimation in various contexts so that students can:

1) compute with whole numbers, fractions, decimals, integers, and rational numbers;
2) develop, analyze, and explain procedures for computation and techniques for estimation;
3) develop, analyze, and explain methods for solving proportions;
4) select and use an appropriate method for computing from among mental arithmetic, paper-and-pencil, calculator, and computer methods;
5) use computation, estimation, and proportions to solve problems;
6) use estimation to check the reasonableness of results.

Standard 8: Patterns and Functions

In grades 5-8, the mathematics curriculum should include explorations of patterns and functions so that students can:

1) describe, extend, analyze, and create a wide variety of patterns;
2) describe and represent relationships with tables, graphs, and rules;
3) analyze functional relationships to explain how a change in one quantity results in a change in another;
4) use patterns and functions to represent and solve problems.

Standard 10: Statistics

In grades 5-8, the mathematics curriculum should include explorations of statistics in real-world situations so that students can:

1) systematically collect, organize, and describe data;
2) construct, read, and interpret tables, charts, and graphs;
3) make inferences and convincing arguments that are based on data analysis;
4) evaluate arguments that are based on data analysis;
5) develop an appreciation for statistical methods as powerful means for decision making.

Standard 13: Measurement

In grades 5-8, the mathematics curriculum should include extensive concrete experiences using measurement so that students can:

1) extend their understanding of the process of measurement;
2) estimate, make, and use measurement to describe and compare phenomena;
3) select appropriate units and tools to measure to the degree of accuracy required in a particular situation;
4) understand the structure and use of systems of measurement;
5) extend their understanding of the concepts of perimeter, area, volume,  angle measure, capacity, and weight and mass;
6) develop the concepts of rate and other derived and indirect measurements;
7) develop formulas and procedures for determining measures to solve problems.