**Make sense of problems and persevere in solving them**

- Consider or attempt multiple entry points
- Analyze information (givens, constraints, relationships, goals)
- Make conjectures and plan a solution pathway
- Use objects, drawings and diagrams to solve problems
- Monitor progress an change course as necessary
- Check answers to problems and ask, “Does this make sense?”

**Reason abstractly and quantitatively**

- Make sense of quantities and relationships in problem situations
- Represent abstract situations symbolically
- Create a coherent representation of the problem
- Translate from contextualized to generalized or vice versa
- Flexibly use properties of operations

**Construct viable arguments and critique**

- Use definitions and previously established causes/effects (results) in constructing arguments
- Listen to or read the arguments of others
- Ask probing questions to other students
- Make conjectures and use counterexamples to build a logical progressions of statements to explore and support their ideas

**Model with mathematics**

- Determine equation that represents a situation
- Illustrate mathematical relationships using diagrams, two-way tables, graphs, flowcharts, and formulas
- Apply assumptions to make a problem simpler
- Check to see if any answer makes sense within the context of a situation and change a model when necessary

**Use Appropriate tools strategically**

- Choose tools that are appropriate for the task. Examples: Manipulatives, calculators, rulers and digital technology
- Use technological tools to visualize the results of assumptions, explore consequences, and compare predictions with data

**Attend to Precision**

- Communicate precisely using appropriate terminology
- Specify units of measure and provide accurate labels on graphs
- Express numerical answers with appropriate degree of precision
- Provide carefully formulated explanations

**Look for and make sue of structure**

- Look for patterns or structure, recognizing that quantities can be represented in different ways
- Use knowledge of properties to efficiently solve problems
- View complicated quantities both as single objects or compositions of several objects

**Look for and express regularity in repeated reasoning**

- Notice repeated calculations and look for general methods and shortcuts
- Continually evaluate the reasonableness of intermediate results while attending to details and make generalizations based on findings