Math standards

The National Council of Teachers of Mathematics has created a set of standards for K-12 math in the following areas -- examples given below are for middle school (grades 6-8):
 * Number and Operations:
 * work flexibly with fractions, decimals, and percents to solve problems;
 * compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line;
 * develop meaning for percents greater than 100 and less than 1;
 * understand and use ratios and proportions to represent quantitative relationships;
 * develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation;
 * use factors, multiples, prime factorization, and relatively prime numbers to solve problems;
 * develop meaning for integers and represent and compare quantities with them.
 * Algebra:
 * represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules;
 * relate and compare different forms of representation for a relationship;
 * identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations.
 * Geometry:
 * precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties;
 * understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects;
 * create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.
 * Measurement:
 * understand both metric and customary systems of measurement;
 * understand relationships among units and convert from one unit to another within the same system;
 * understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume.
 * Data Analysis & Probability:
 * formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population;
 * select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.

They also include K-12 wide Process Standards for:


 * Problem Solving: Instructional programs from prekindergarten through grade 12 should enable all students to
 * Build new mathematical knowledge through problem solving
 * Solve problems that arise in mathematics and in other contexts
 * Apply and adapt a variety of appropriate strategies to solve problems
 * Monitor and reflect on the process of mathematical problem solving


 * Reasoning and Proof: Instructional programs from prekindergarten through grade 12 should enable all students to -
 * Recognize reasoning and proof as fundamental aspects of mathematics
 * Make and investigate mathematical conjectures
 * Develop and evaluate mathematical arguments and proofs
 * Select and use various types of reasoning and methods of proof


 * Communication: Instructional programs from prekindergarten through grade 12 should enable all students to -
 * Organize and consolidate their mathematical thinking through communication
 * Communicate their mathematical thinking coherently and clearly to peers, teachers, and others
 * Analyze and evaluate the mathematical thinking and strategies of others;
 * Use the language of mathematics to express mathematical ideas precisely.


 * Connections: Instructional programs from prekindergarten through grade 12 should enable all students to -
 * Recognize and use connections among mathematical ideas
 * Understand how mathematical ideas interconnect and build on one another to produce a coherent whole
 * Recognize and apply mathematics in contexts outside of mathematics


 * Representation: Instructional programs from prekindergarten through grade 12 should enable all students to -
 * Create and use representations to organize, record, and communicate mathematical ideas
 * Select, apply, and translate among mathematical representations to solve problems
 * Use representations to model and interpret physical, social, and mathematical phenomena