School Improvement in Maryland

The Processes of Mathematics


  • Justify why an answer or approach to a problem is reasonable;
  • Make and test generalizations based upon investigation or observation;
  • Make predictions or draw conclusions from available information;
  • Analyze statements and provide examples which support or refute them;
  • Judge the validity of arguments by applying inductive(1) and deductive(2) thinking;
      (1) inductive: inference by reasoning from the specific to the general.
      (2) deductive: inference by reasoning from the general to the specific.
  • Use supporting data to explain why a chosen method used and a solution are mathematically correct.


  • Identify and use the relationships among mathematical concepts as a basis for learning additional concepts;
  • Identify the relationships among graphical, numerical, physical, and algebraic mathematical models and concepts;
  • Identify mathematical concepts and processes as they apply to other content areas;
  • Use mathematical concepts and processes to translate personal experiences into mathematical language.


  • Use multiple representations to express mathematical concepts and solutions;
  • Represent problem situations and express their solutions using pictorial, tabular, graphical, and algebraic methods;
  • Use mathematical language and symbolism appropriately;
  • Describe situations mathematically by providing mathematical ideas and evidence in written form;
  • Present results in written form.

Problem Solving

  • Use information to identify and define the question(s) within a problem;
  • Make a plan and decide what information and steps are needed to solve the problem;
  • Choose the appropriate operation(s) for a given problem situation;
  • Select and apply appropriate problem-solving strategies to solve a problem from visual (draw a picture, create a graph), numerical (guess and check, look for a pattern), and symbolic (write an equation) perspectives;
  • Organize, interpret, and use relevant information;
  • Select and use appropriate tools and technology;
  • Show that no solution or multiple solutions may exist;
  • Identify alternate ways to find a solution;
  • Apply what was learned to a new problem.