NCTM Mathematics Curriculum Standards for Digital Images: from Satellites to the Internet
Standard 1
Mathematics as Problem Solving
Standard 3
Mathematics as Reasoning 
Standard 8
Patterns and Functions

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 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.