**Reasoning**

- Justify why an answer or approach to a problem is reasonable;
- Make and test generalizations based upon investigation or observation;
- Make predictions or draw conclusions from available information;
- Analyze statements and provide examples which support or refute them;
- Judge the validity of arguments by applying inductive
^{(1)}and deductive^{(2)}thinking;^{(1)}inductive: inference by reasoning from the specific to the general.

^{(2)}deductive: inference by reasoning from the general to the specific. - Use supporting data to explain why a chosen method used and a solution are mathematically correct.

**Connections**

- Identify and use the relationships among mathematical concepts as a basis for learning additional concepts;
- Identify the relationships among graphical, numerical, physical, and algebraic mathematical models and concepts;
- Identify mathematical concepts and processes as they apply to other content areas;
- Use mathematical concepts and processes to translate personal experiences into mathematical language.

**Communications**

- Use multiple representations to express mathematical concepts and solutions;
- Represent problem situations and express their solutions using pictorial, tabular, graphical, and algebraic methods;
- Use mathematical language and symbolism appropriately;
- Describe situations mathematically by providing mathematical ideas and evidence in written form;
- Present results in written form.

**Problem Solving**

- Use information to identify and define the question(s) within a problem;
- Make a plan and decide what information and steps are needed to solve the problem;
- Choose the appropriate operation(s) for a given problem situation;
- Select and apply appropriate problem-solving strategies to solve a problem from visual (draw a picture, create a graph), numerical (guess and check, look for a pattern), and symbolic (write an equation) perspectives;
- Organize, interpret, and use relevant information;
- Select and use appropriate tools and technology;
- Show that no solution or multiple solutions may exist;
- Identify alternate ways to find a solution;
- Apply what was learned to a new problem.