Math standards

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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