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The 8 Standards for Mathematical Practice

(How Good Mathematicians Do Math)

The Standards for Mathematical Practice are how good mathematicians do math.  These are the habits math teachers strive to develop in their students.  Students become mathematically proficient in engaging with mathematical content and concepts as they learn, experience, and apply these skills and attitudes

Standard for Math Practice 1

Make sense of problems and persevere in solving them.

Explain the meaning of a problem and look for different ways to solve them.  Make predictions and estimates about the solution. Identify and analyze the information given, constraints, and relationships.  Form a plan to problem solve, and continually monitor progress asking, “Does this make sense?” Consider similar problems, make connections between multiple representations, and identify the relationships and similarities between different approaches.  Check answers to problems using a different method.

Standard for Math Practice 2

Reason abstractly and quantitatively.

Make sense of the quantities (numbers and variables) and their relationships in problem situations. Translate between context (story) and algebraic representations. This includes the ability to read a story problem, write an algebraic expression or equation for it, solve or simplify the algebra, then relate it back to the original situation.

Standard for Math Practice 3

Construct viable arguments and critique the reasoning of others.

Write out and complete the steps necessary to solve a problem.  Justify your thoughts or solutions.  Explain your thinking to others.  Respond to the arguments of others by listening, asking clarifying questions, and critiquing the reasoning of others.

Standard for Math Practice 4

Model with mathematics.

Apply mathematics to solve problems arising in everyday life, society, and the workplace. Identify important quantities and construct a mathematical model (equation, graph, table, picture, symbols, etc.). Interpret mathematical results in the context of the situation and decide on whether the results make sense and improve the model if it doesn’t.

Standard for Math Practice 5

Use appropriate tools strategically.

Consider the available tools and be sufficiently familiar with them to make sound decisions about when each tool might be helpful, recognizing both the insight to be gained as well as the limitations. Use tools like technology or manipulatives to explore and deepen their understanding of concepts.

Standard for Math Practice 6

Attend to precision.

Communicate precisely to others. Use explicit definitions in discussion with others and in their own reasoning. Know the names of symbols used. Specify units of measure and label axes to clarify the correspondence with quantities in a problem. Calculate accurately and efficiently. Express numerical answers with a degree of precision appropriate for the problem context (round when necessary for the situation).

Standard for Math Practice 7

Look for and make use of structure.

Look closely at mathematical relationships to identify the underlying structure by recognizing a simple, more familiar processes within a more complicated structure. Look closely to discern patterns and recognize the significance of mathematical features.  See complicated scenarios as a single object or as composed of several objects.  Making use of structure can make new information make more sense.  For example:

5 + 2 = 7, so it makes sense that 5 hundred + 2 hundred = 7 hundred, or in other words, 500 + 200 = 700.

Standard for Math Practice 8

Look for and express regularity in repeated reasoning.

Notice if reasoning is repeated, and look for both generalizations and shortcuts. Evaluate the reasonableness of intermediate results by maintaining oversight of the process while attending to the details.  Notice if calculations are repeated and look for general methods and shortcuts.  Make asusmptions based on patterns.