1. Standards for Mathematical Practice
Make sense of problems and persevere in solving them.
First explain meaning of problem to themselves
Analyze, conjecture, plan
Consider analogous problems
Try simpler forms of the original problem
Can explain correspondence between graphs,
charts/tables, verbal descriptions, equations
Check their answers
Understand approaches of others; see correspondences
between the various approaches

2. Standards for Mathematical Practice
Reason abstractly and quantitatively.
Make sense of quantities and their relationships in problem situations
Have ability to both decontextualize (abstract a given situation and represent it symbolically) and to contextualize (consider the actual meaning of the various parts of the situation)
Ability to create a coherent representation of the problem – consider units involve, meaning of quantities as well as how to compute them
Know and flexibly use different properties of operations and objects

3. Standards for Mathematical Practice
Construct viable arguments and critique the reasoning of others.
Understand and use state assumptions, definitions, previously established results in constructing arguments
Make conjectures and build logical progression of statements to explore the truth of those conjectures
Analyze situations by breaking them into cases
Recognize and use counter examples
Justify conclusions
Reason inductively about data
Compare effectiveness of two plausible arguments
Read/analyze/question the arguments of others

4. Standards for Mathematical Practice
Model with mathematics.
Apply known mathematics to solve real world problems
Can comfortably make assumptions and approximations to simplify complicated situations
Realize such assumptions/approximations may require later adjustment
Identify important quantities and map their relationships using a variety of tools: diagrams, two-way tables, graphs, flowcharts, formulas
Can analyze relationships mathematically to draw conclusions
Routinely interpret the results in the context of the situation
Reflect on whether the results make sense

5. Standards for Mathematical Practice
Use appropriate tools strategically.
Consider available tools when solving mathematical problems: pencil/paper, concrete models, ruler, protractor, calculator, spread-sheet, computer algebra system, dynamic geometry software, etc.
Sufficiently familiar with tools to recognize the insight that can be gained from their use and their limitations
Strategically use estimation to detect possible errors
Identify relevant external mathematical resources (websites, etc.) and use them effectively
Able to use technological tools to explore and deepen understanding of concepts

6. Standards for Mathematical Practice
Attend to precision.
Communicate precisely to others
Use clear definitions in discussion with others and in their own reasoning
State meaning of symbols they choose (including equal sign) consistently and appropriately
Specify units of measures and label axes to clarify correspondence with quantities in a problem
Calculate accurately and efficiently
Express numerical answers with appropriate degree of precision
Provide carefully formulated explanations
By high school – examine claims and explicitly use definitions.

7. Standards for Mathematical Practice
Look for and make use of structure.
Examine carefully to discern pattern or structure
Early: more is same as more
Early: Sort shapes by number of sides
Later: 7 x 8 equals 7 x x 3
Later: x2 (squared) + 9x + 14 – can see the 9 as and the 14 as 2 x 7
Recognize significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems
Can step back for overview and shift perspective
View complicated items as single objects or as being composed of several objects

8. Standards for Mathematical Practice
Look for and express regularity in repeated reasoning
Notice if calculations are repeated
Look for both general methods and shortcuts
Example: recognize repeating decimal when dividing 25 by 11
Example: abstract equation (y-2)/(x-1)=3 by paying attention to the calculation of slope when repeatedly checking whether points are on the line through (1,2) with slope 3
Maintain oversight of the process, while attending to details
Continually evaluate reasonableness of their intermediate results