- 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
- recognize reasoning and proof as fundamental aspects of mathematics
- organize and consolidate 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
- 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
- select, apply and translate among mathematical representation to solve problems

- understand numbers, multiple ways of representing numbers, relationships among numbers and number systems
- understand operations and procedures and how they relate to one another
- compute accurately and make reasonable estimates
- represent and analyze algebraically a wide variety of problem solving situations
- use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes
- determine what can be measured and how, using appropriate measures and formulas
- collect, organize, display and analyze data

- understand numbers, multiple ways of representing numbers, relationships among numbers and number systems
- understand meanings of operations and procedures and how they relate to one another
- represent and analyze algebraically a wide variety of problem solving situations
- perform algebraic procedures accurately
- recognize, use and represent algebraically patterns, relations and functions
- use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes
- identify and justify geometric relationships, formally and informally
- apply coordinate geometry to analyze problem solving situations
- determine what can be measured and how, using appropriate methods and formulas
- develop strategies for estimating measurements
- collect, organize, display and analyze data
- understand and apply concepts of probability

- understand operations and procedures, and how they relate to one another
- represent and analyze algebraically a wide variety of problem solving situations
- perform algebraic procedures accurately
- recognize, use and represent algebraically patterns, relations and functions
- use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes
- identify and justify geometric relationships, formally and informally
- apply transformations and symmetry to analyze problem-solving situations
- apply coordinate geometry to analyze problem solving situations
- determine what can be measured and how, using appropriate methods and formulas