National Math Standards (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:

· formulate problems from situations within and outside mathematics.

· develop and apply a variety of strategies to solve problems, with emphasis on
  multi-step and non-routine problems.

· verify and interpret results with respect to the original problem situation.

· generalize solutions and strategies to new problem situation.

· acquire confidence in using mathematics meaningfully.

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 and clarify their own thinking about mathematical ideas and situations.

· use the skills of reading, listening, and viewing to interpret and evaluate mathematical ideas.

Standard 3: Mathematics as Reasoning

Reasoning shall permeate the mathematic curriculum so that students can:

· understanding and apply reasoning processes, with special attention to spatial reasoning and reasoning with proportions and graphs.

The mathematics curriculum should include the investigation of mathematical connections so that students can:

· 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.

The mathematics curriculum should include the continued development of number and number relationships so that students can:

· understand, represent, and use numbers in a variety of equivalent forms (integer, fraction, decimal, percent, exponential, and scientific notation) in real-world and mathematical problem situations.

· understand and apply ratios, proportions, and percents in a wide variety of situations.

· represent numerical relationships in one- and two-dimensional graphs.

The mathematics curriculum should develop the concepts underlying computation and estimation in various contexts so that students can:

· develop, analyze, and explain procedures for computation and techniques for estimation.

· develop, analyze, and explain methods for solving proportions.

· use computation, estimation, and proportions to solve problems.

· use estimation to check the reasonableness of results.

The mathematics curriculum should include explorations of patterns and functions so that students can:

· describe, extend, analyze, and create a wide variety of patterns.

· analyze functional relationships to explain how a change in one quantity results in a change in another.

The mathematics curriculum should include exploration of statistics in real-world situations so that students can:

· systematically collect, organize, and describe data.

· make inference and convincing arguments that are based on data analysis.

· evaluate arguments that are based on data analysis.

· develop an appreciation for statistical methods as powerful means for decision making.

The mathematical curriculum should include explorations of probability in real-world situations so that students can:

· make predictions that are based on experiment or theoretical probabilities.

The mathematical 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 concepts of perimeter, area, volume, angle measure, capacity, and weight and mass.

· develop formulas and procedures for determining measures to solve problems.