This Standards Refresher is based on the Principles and Standards for School Mathematics, developed by the National Council of Teachers of Mathematics (NCTM).

**Standard**

**What Is It?**

Number and Operations (includes Arithmetic and Number Sense)

Arithmetic includes addition, subtraction, multiplication, and division of integers, decimals, and fractions. Number sense includes knowing basic facts as well as the ability to compare numbers, estimate, and use equivalent representations of quantities to solve math problems.

Patterns, Relationships, and Algebraic Thinking

Algebra is a generalization of arithmetic. It includes identifying, representing, and using relationships and patterns. Often letters represent numbers in math expressions to describe relationships.

Geometry and Spatial Visualization

Geometry includes recognizing, representing, describing, and relating shapes and solids and their characteristics in space. It includes plotting points in a coordinate system.

Measurement

Measurement uses standard units to indicate size such as length, area, volume, time, or other quantities.

Probability and Statistics

Probability and Statistics are areas of math that relate to using data to make decisions. Probability concerns the likelihood that something will happen, usually expressed as a fraction or a percentage. Statistics is the collection, organization, and analysis of data.

Problem Solving

Problem solving is a central activity of math; it involves creating and using strategies to solve problems, self-monitoring by checking work, and building knowledge through exploring problems.

Reasoning and Proof

Reasoning and Proof refers to understanding mathematical arguments and applying ways to assess the validity of those arguments. Frequently this process is referred to as finding (or developing) proofs.

Communication

Communication refers to using the language of mathematics productively and accurately. This applies when presenting ideas to others, listening and evaluating, or consolidating one's own thinking.

Connections

The Connections standard is the concept that mathematical ideas and processes are inherently interrelated both within mathematics and to contexts outside of mathematics.

Representation

Representation is the ability to use forms of presentation (graphs, equations, or diagrams, for instance) to organize mathematical thinking, solve problems, and present or interpret ideas.