National Council for Teachers of Mathematics Curriculum Standards Go back to lesson. 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-- use problem-solving approaches to investigate and understand mathematical content; formulate problems from situations within and outside mathematics; develop and apply a variety of strategies to solve problems, with emphasis on multistep and nonroutine problems; verify and interpret results with respect to the original problem situation; generalize solutions and strategies to new problem situations; acquire confidence in using mathematics meaningfully. STANDARD 2. MATHEMATICS AS COMMUNICATION In grades 5-8, the study of mathematics should include opportunities to communicate so that students can-- model situations using oral, written, concrete, pictorial, graphical, and algebraic methods; reflect on and clarify their own thinking about mathematical ideas and situations; develop common understandings of mathematical ideas, including the role of definitions; use the skills of reading, listening, and viewing to interpret and evaluate mathematical ideas; discuss mathematical ideas and make conjectures and convincing arguments; 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-- recognize and apply deductive and inductive reasoning; understand and apply reasoning processes, with special attention to spatial reasoning and reasoning with proportions and graphs; make and evaluate mathematical conjectures and arguments; validate their own thinking; appreciate the pervasive use and power of reasoning as a part of mathematics. STANDARD 4. MATHEMATICAL CONNECTIONS In grades 5-8, the mathematics curriculum should include the investigation of mathematical connections so that students can-- see mathematics as an integrated whole; explore problems and describe results using graphical, numerical, physical, algebraic, and verbal mathematical models or representations; use a mathematical idea to further their understanding of other mathematical ideas; apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as art, music, psychology, science, and business; value the role of mathematics in our culture and society. STANDARD 8. PATTERNS AND FUNCTIONS In grades 5-8, the mathematics curriculum should include explorations of patterns and functions so that students can-- describe, extend, analyze, and create a wide variety of patterns; describe and represent relationships with tables, graphs, and rules; analyze functional relationships to explain how a change in one quantity results in a change in another; use patterns and functions to represent and solve problems. STANDARD 9. ALGEBRA In grades 5-8, the mathematics curriculum should include explorations of algebraic concepts and processes so that students can- understand the concepts of variable, expression, and equation; represent situations and number patterns with tables, graphs, verbal rules, and equations and explore the interrelationships of these representations; analyze tables and graphs to identify properties and relationships; develop confidence in solving linear equations using concrete, informal, and formal methods; investigate inequalities and nonlinear equations informally; apply algebraic methods to solve a variety of real-world and mathematical problems. STANDARD 12. GEOMETRY In grades 5-8, the mathematics curriculum should include the study of the geometry of one, two, and three dimensions in a variety of situations so that students can-- identify, describe, compare, and classify geometric figures; visualize and represent geometric figures with special attention to developing spatial sense; explore transformations of geometric figures; represent and solve problems using geometric models; understand and apply geometric properties and relationships; develop an appreciation of geometry as a means of describing the physical world. STANDARD 13. MEASUREMENT In grades 5-8, the mathematics curriculum should include extensive concrete experiences using measurement so that students can-- extend their understanding of the process of measurement; estimate, make, and use measurements to describe and compare phenomena; select appropriate units and tools to measure to the degree of accuracy required in a particular situation; understand the structure and use of systems of measurement; extend their understanding of the concepts of perimeter, area, volume, angle measure, capacity, and weight and mass; develop the concepts of rates and other derived and indirect measurements; develop formulas and procedures for determining measures to solve problems.