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.