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Problem Solving Tips!

There are four stages in solving a given problem. Each problem may involve one or more of the suggested strategies.

The four stages were developed by George Polya, a Hungarian mathematician. We also incorporate the Socratic Method which is a series of Q&A, to check one's critical thinking, logic and reasoning, as we seek to find any holes in the process.

Understanding the Problem

  • Read the problem carefully
  • List the details you know
  • Look for phrases
  • Pick out the important information
  • State the problem in your own words

Analyzing the Problem

  • Look for a pattern
  • Draw a picture
  • Use models or act out the problem
  • Make an organized list
  • Guess and test
  • State and solve an equation
  • Use logical reasoning
  • Consider a simpler form of the problem
  • Work the problem backward

Doing the Necessary Computations

  • Simplify any arithmetic expressions
  • Solve any algebraic equations
  • Use a calculator or computer as appropriate

Providing the Desired Results

  • Answer all questions
  • Provide all requested information
  • Be sure all results (solutions) are reasonable
  • Check all solutions
  • Look for extensions or generalizations of the solutions
  • State the problem and its solution in sentence form
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