GENERAL PROBLEM SOLVING PROCEDURE

1. DEFINE THE PROBLEM
         1.1 UNDERSTAND THE PROBLEM.
         1.2 SPECIFY THE DETAILS OF THE PROBLEM.
         1.3 WRITE A DESCRIPTION OF THE PROBLEM.
2. VISUALIZE THE PROBLEM AND POSSIBLE SOLUTION METHODS
         2.1 DRAW PICTURES OF THE PROBLEM.
         2.2 DRAW DIAGRAMS OF THE PROBLEM.
         2.3 PLAN POSSIBLE SOLUTION METHODS.
              2.3.1 DRAW CONCEPTUAL DIAGRAMS OF POSSIBLE PROCEDURES.
              2.3.2 DRAW PICTURES OF EXPECTED RESULTS FROM SOLUTION METHODS.
3. DESCRIBE WHAT KNOWN RESOURCES ARE AVAILABLE TO PRODUCE RESULTS
         3.1 LABEL ALL PICTURES AND DIAGRAMS WITH THE KNOWN INFORMATION.
         3.2 ASSIGN SYMBOLS TO KNOWN RESOURCES.
         3.3 LIST ALL KNOWN CONDITIONS AND CHARACTERISTICS.
4. IDENTIFICATION OF THE RESULTS TO BE FOUND
         4.1 DESCRIBE WHAT RESULTS ARE NEEDED.
         4.2 DESCRIBE THE UNKNOWNS WHICH NEED TO BE DETERMINED.
         4.3 ASSIGN SYMBOLS TO EACH UNKNOWN DESCRIBED.
5. DESCRIBE THE PROCEDURES AVAILABLE TO PRODUCE THE RESULTS FROM RESOURCES
         5.1 LIST ALL SET OF RULES (IN SYMBOLIC FORM) WHICH RELATE NEEDED
               RESULTS AND RESOURCES.
         5.2 LIST ALL FORMULAS IN SYMBOLIC FORM WHICH CAN BE USED TO
               DETERMINE RESULTS FROM RESOURCES.
         5.3 LIST ALL EQUATIONS IN SYMBOLIC FORM WHICH RELATE NEEDED RESULTS
               TO RESOURCES.
6. SYNTHESIS OF A SOLUTION
         6.1 USE THE AVAILABLE PROCEDURES TO PRODUCE THE DESIRED RESULTS FROM
               THE KNOWN RESOURCES.
         6.2 REPLACE THE SYMBOLS USED IN THE PROCEDURES WITH ACTUAL VALUES OF
               KNOWN QUANTITIES.
         6.3 DETERMINE THE VALUES OF ANY RESULTS WHICH CAN BE FOUND DIRECTLY BY
               FOLLOWING THE RULES OR USING THE FORMULAS AND EQUATIONS.
         6.4 USE THE RESOURCES AND ANY RESULTS NOW AVAILABLE TO DETERMINE OTHER
               RESULTS.
         6.5 USE THE AVAILABLE PROCEDURES (USING TRIAL AND ERROR WHEN
               NECESSARY) TO DETERMINE THE REMAINING NEEDED RESULTS FROM THE
               ALREADY CALCULATED RESULTS AND THE KNOWN RESOURCES. USE ALL THE
               PROCEDURES UNTIL ALL THE POSSIBLE COMBINATIONS HAVE BEEN TRIED.
7. EVALUATE THE SOLUTION
         7.1 IS THE SOLUTION POSSIBLE?
         7.2 IS THE SOLUTION REASONABLE?
 

Demonstration of the Use of this Problem Solving Procedure

Steps 1 through 5 are the ANALYSIS OF THE PROBLEM.
Steps 6 and 7 are the SYNTHESIS OF A SOLUTION.

For Example:

I. Find the length of the side of a cube shaped block of copper which weighs 49 Newtons.

II & III                    copper cube
                                W = 49 N
                                g= 9.81 m/s2
                                D = 8920 kg/m3
 

                                   l = w = h = a


                  a

IV.    a = ?
         m = ?
         V= ?

V.     D = m/V

         W = mg
         V= a3

VI.     D = m/V
   so    DV = m
and    V = m/D
also     W = mg
  so    m = W/g
Therefore V= (W/g)/D
but    W = 49 N
          g= 9.81 m/s2
 and    D = 8920 kg/m3

so     V = [(49/9.81)/8920] m3

but    V= a3

so     a = V1/3

Therefore     a= {[(49/9.81)/8920]}1/3 m

        and       a = 0.0824 m or 8.24 cm.

VII. length a is possible
        length a is reasonable