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.