Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique
Model with mathematics
Use Appropriate tools strategically
Attend to Precision
Look for and make sue of structure
Look for and express regularity in repeated reasoning
- 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