How to Use Problem Solving and Posing Strategies

Step-by-Step Guide

1. 1

   Step 1: Understand the problem Find

   Find out if it is possible to satisfy the condition? Is the condition sufficient to determine the unknown? Or is it insufficient? Or redundant? Separate the various parts of the condition.
   
   Can you write them down Draw a figure.
   
   Introduce suitable notation.
2. 2

   Step 2: specify and clearly define the unknowns

   You may be obliged to consider auxiliary problems if an immediate connection cannot be found.
   
   You should eventually obtain a plan of the solution.
   
   Decide if you have seen it before in a slightly different form? Or have you seen the same problem in different situations/conditions? Do you know a related problem? Do you know a theorem that could be useful? Look at the unknown, and try to think of a familiar problem having the same or a similar unknown.
   
   Try to use the information, solution ideas, results and methods that were used on the related/similar problem you found in the previous steps.
   
   Should you introduce some auxiliary element in order to make its use possible? Try to restate the problem if that doesn't work.
   
   Could you restate it still differently? Go back to definitions.
   
   Try to solve some related problem first if you cannot solve the proposed problem.
   
   Could you imagine a more accessible related problem? A more general problem? A more special problem? An analogous problem? Could you solve a part of the problem? Keep only a part of the condition, drop the other part; how far is the unknown then determined, how can it vary? Could you derive something useful from the data? Could you think of other data appropriate to determine the unknown? Could you change the unknown or data, or both if necessary, so that the new unknown and the new data are nearer to each other? Try to revise the following points if that still fails:
   Did you use all the data? Did you use the whole condition? Have you taken into account all essential notions involved in the problem? , Can you see clearly that the step is correct? Can you prove that it is correct? Look back.
   
   Examine the solution obtained.
   
   Can you check the result? Can you check the argument? Can you derive the solution differently? Can you see it at a glance? Can you use the result, or the method, for some other problem?
3. 3

   Step 3: data and conditions.

4. 4

   Step 4: Devise a plan Find the connection between the data and the unknown.

5. 5

   Step 5: Carry out the plan Check each step.

Detailed Guide

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