# Mathematics

The abstract science of number, quantity, and space.

## Look for and express regularity in repeated reasoning.

Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts.

## Look for and make use of structure.

Mathematically proficient students look closely to discern a pattern or structure.

## Attend to precision.

Mathematically proficient students try to communicate precisely to others.

## Use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a mathematical problem.

## Model with mathematics.

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.

## Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures.

## Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations.

## Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals.

## Standards for Mathematical Practice Introduction

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students.