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There are five steps to problem solving:

1) understanding

2) organization

3) strategy

4) execution

5) reflection

Step 1: Picture the problem (Understanding)

Read the problem carefully to know what is known and what is not known. Understand the objective of the problem. Write down what is known and what needs to be solved.

Step 2: Get organized (Organization)

Separate the relevant and irrelevant parts of the presented information, and eliminate the irrelevant information. Translate words into the mathematical language. Introduce variables for the unknown quantities discussed. Attempt to obtain more information from prior knowledge, or by dabbling with the information given in the problem. Make correct connections between the gathered information in order to develop testable assumptions. If a diagram will help, draw the diagram (this is especially important when solving physics or geometry problems). Be sure the diagrams are labeled with the information.

Step 3: Develop a plan (Strategy)

Conjure up a process for solving the problem with well thought out steps. These steps will vary depending on the problem. Strategies may vary from starting with a simpler problem to working backwards.

Step 4: Solve the problem (Execution)

Carry out the strategy. Work out the steps detailed in the plan. Methods will vary.

Step 5: Check and reflect (Reflection)

Verify the correctness of the answer from the steps that led to the answer. Were mistakes made along the way? Do the results make sense? For the sake of curiosity, think about other ways of solving the problem. Are there any extensions to the problem?