Polya’s 4 Steps to Problem Solving

  1. Understanding the Problem:
  • Try to make a sketch to illustrate the problem. Label the information given.
  • Make a list of the given facts. Are they all pertinent to the problem?
  • Determine if the information you are given is sufficient to solve the problem.
  1. Devise a plan to solve the problem
  • Have you seen the problem or a similar problem before?
  • Are the procedures you used to solve the similar problem applicable to the new problem?
  • Can you express the problem in terms of an algebraic equation?
  • Look for patterns or relationships in the problem that may help in solving it.
  • Can you express the problem more simply?
  • Will listing the information in a table help?
  • Can you substitute smaller or simpler numbers to make the problem more understandable?
  • Can you make an educated guess at the solution?
  • Sometimes if you know an approximate solution, you can work backwards and eventually determine the correct procedure to solve the problem.
  1. Carry out and monitor your plan
  • Use the plan you devised in step 2 to solve the problem.
  • Check frequently to see whether it is productive or is going down a dead-end street. If unproductive, revisit Step 2.
  1. Look back at your work and check your results
  • Ask yourself, “Does the answer make sense?” and “Is the answer reasonable?”
  • If the answer is not reasonable, recheck your method for solving the problem and your calculations.
  • Can you check the solution using the original statement?
  • Is there an alternative method to arrive at the same conclusion?
  • Can the results of this problem be used to solve other problems?

Acute angle: measures less than 90o Right angle: measures 90o

Obtuse angle: measures more than 90o Straight angle: measures 180o

Adjacent angles: share a common ray Sum of the angles inside a

triangle is 180o

Complimentary angles: add to 90o Supplementary angles: add to 180o

Solve for x

Solve for x

Solve for x

Parallel Lines never meet

They are always equidistance apart.

Notation l1 || l2

Vertical angles are equal Alternate interior angles are equal

Consecutive interior angles are supplementary

Alternate exterior angles are equal

Corresponding angles are equal

Solve for x.

Solve for x.

Solve for x.

Solve for x.

Solve for x.

Solve for x.