NCTM Mathematics Curriculum Standards for Every Picture Tells a Story (5-8)
Standard 1 
Mathematics as Problem Solving
Standard 2 
Mathematics as Communication
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 2: Mathematics as Communication 

In grades 5-8, the mathematics curriculum should include opportunities to communicate so that students can: 

1) model situations using oral, written, concrete, pictorial, graphical, and algebraic methods; 
2) reflect on and clarify their own thinking about mathematical ideas and situations; 
3) develop common understandings of mathematical ideas, including the role of definitions; 
4) use the skills of reading, listening, and viewing to interpret and evaluate mathematical ideas; 
5) discuss mathematical ideas and make conjectures and convincing arguments; 
6) appreciate the value of mathematical notation and its role in the development of mathematical ideas. 

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.