Number and operations

• Understand numbers, ways of representing numbers, relationships among numbers, and number systems

• Understand meanings of operations and how they relate to one another

• Compute fluently and make reasonable estimates

Algebra

• Understand patterns, relations, and functions

• Represent and analyze mathematical situations and structures using algebraic symbols

• Use mathematical models to represent and understand quantitative relationships

• Analyze change in various contexts

Geometry

• 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

• Use visualization, spatial reasoning, and geometric modeling to solve problems

Measurement

• Understand measurable attributes of objects and the units, systems, and processes of measurement

• Apply appropriate techniques, tools, and formulas to determine measurements

Data analysis and probability

• 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

• Understand and apply basic concepts of probability

Problem solving

• 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

• 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

• Organize and consolidate mathematical thinking through communication

• Communicate 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