National Council of
Teachers of Mathematics’
Standards for School Mathematics:
Pre-Kindergarten through Grade 12*

Instructional programs from prekindergarten through grade 12 should enable all students to:

Number and Operations Standard:

• Understand numbers, ways of representing numbers, relationships among numbers, and number systems;
• Understand meanings of operations and how they relate to one another; and
• Compute fluently and make reasonable estimates.

Measurement Standard:

• Understand measurable attributes of objects and the units, systems, and processes of measurement; and
• Apply appropriate techniques, tools, and formulas to determine measurements.

Geometry Standard:

• Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships;
• Specify locations and describe spatial relationships using coordinate geometry and other representational systems;
• Apply transformations and use symmetry to analyze mathematical situations; and
• Use visualization, spatial reasoning, and geometric modeling to solve problems.

Algebra Standard:

• Understand patterns, relations, and functions;
• Represent and analyze mathematical situations and structures using algebraic symbols;
• Use mathematical models to represent and understand quantitative relationships; and
• Analyze change in various contexts.

Data Analysis and Probability Standard:

• Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them;
• Select and use appropriate statistical methods to analyze data;
• Develop and evaluate inferences and predictions that are based on data; and
• Understand and apply basic concepts of probability.

Process Standards:

• Instructional programs for prekindergarten through grade 12 should enable students to:

Problem Solving Standard:

• 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; and
• Monitor and reflect on the process of mathematical problem solving

Reasoning and Proof Standard:

• Recognize reasoning and proof as fundamental aspects of mathematics; make and investigate mathematical conjectures;
• Develop and evaluate mathematical arguments and proofs; and
• Select and use various types of reasoning and methods of proof.

Communication Standard:

• 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; and
• Use the language of mathematics to express mathematical ideas precisely.

Connections Standard:

• Recognize and use connections among mathematical ideas;
• Understand how mathematical ideas interconnect and build on one another to produce a coherent whole; and
• Recognize and apply mathematics in contexts outside of mathematics.

Representation Standard:

• Create and use representations to organize, record, and communicate mathematical ideas;
• Select, apply and translate among mathematical representations to solve problems; and
• Use representations to model and interpret physical, social, and mathematical phenomena.

* from Principles and Standards for School Mathematics