# 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