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Introduction to the 8 Mathematical Practices

The 8 Standards of Mathematical Practice, Part 1
via ytCropper

Make sense of problems and persevere in solving them

  • Explain the meaning of a problem, look for a way to begin
  • Analyze and make a plan
  • Monitor progress and adapt
  • Use various mathematical representations/tools to explain
  • Find a solution pathway – does it make sense?
  • Persevere & work hard to solve/attempt differentmethods

Reason abstractly and quantitatively

  • Ability to abstract a given idea (turn it into numbers or variables)
  • Explanations show careful reasoning and deep thinking
  • Create a meaningfulrepresentation considering units involved
  • Represent the problemwith symbols, graphs, tables, or functions
  • Flexibly use different properties of operations
  • Show understanding of numbers and the quantities they represent

The 8 Mathematical Practices, Part 2

Construct viable arguments and critique the reasoning of others

  • Use prior learning to analyze situations
  • Communicate conclusions & respond to arguments of others
  • Use evidence and reasoning to create logical arguments
  • Debate reasonableness of arguments without attacking
  • Make connections among different ideas in math and between other subjects

Model with mathematics

  • Can apply mathematics to everyday situations & real numbers
  • Apply assumptions and approximations where appropriate
  • Use a variety of math tools to map or diagram important relationships between quantities (flow charts, tables, and functions)
  • Interpret results and possibly make improvements
  • Ability to express scenarios in mathematical language and symbols and choose the best representation for each situation

Use appropriate tools strategically

  • Awareness of math resources such as technology, concrete models or previous learning
  • Be familiar with a wide variety of ways to represent & solve problems
  • Use technological tools to deepen understanding
  • Make deliberate choices of which math tool to use to best solve problems
  • Strategically use estimation as a tool to solve and check work


 The 8 Mathematical Practices, Part 3

Attend to precision

  • Use clear definitions and accurate terminology in communication, state the meaning of symbols, specify units of measure, and calculate accurately
  • Use complete and appropriate labels on graphical representations

Look for and make use of structure

  • Make and test conjectures and make generalizations about ideas and methods
  • Comfortably use numerical relationships to build understanding and flexibility with numbers
  • Break complicated problems down into simpler components (solve an easier problem)
  • Use previous knowledge of patterning/structure to help solve problems

Look for and express regularity in repeated reasoning

  • Ability to use and recognize patterns to simplify solutions
  • Recognize repeated calculations and how they relate to problem-solving strategies
  • Keep the big picture in mind and attend to details
  • Evaluate the reasonableness of the answer
  • Explanations show deeper and broader understandings of math concepts

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