### Discuss the problem-solving process outlined

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Discuss the Problem-Solving Process outlined. Which step is the most important? Could students solve problems without one of these steps? Give an example of a problem and demonstrate its solution through the four steps.

Four-Step Problem-Solving Process

1. Understanding the problem

a. Can you state the problem in your own words?

b. What are you trying to find or do?

c. What are the unknowns?

d. What information do you obtain from the problem?

e. What information, if any, is missing or not needed?

2. Devising a plan

The following list of strategies, although not exhaustive, is very useful:

a. Look for a pattern.

b. Examine related problems and determine if the same technique applied to them can be applied to the current problem.

c. Examine a simpler or special case of the problem to gain insight into the solution of the original problem.

d. Make a table or list.

e. Make a diagram.

f. Write an equation.

g. Use guess and check.

h. Work backward.

i. Identify a subgoal.

j. Use indirect reasoning.

k. Use direct reasoning.

3. Carrying out the plan

a. Implement the strategy or strategies in step 2 and perform any necessary actions or computations.

b. Check each step of the plan as you proceed.This may be intuitive checking or a formal proof of each step.

c. Keep an accurate record of your work.

4. Looking back

a. Check the results in the original problem. (In some cases, this will require a proof.)

b. Interpret the solution in terms of the original problem. Does your answer make sense? Is it reasonable? Does it answer the question that was asked?

c. Determine whether there is another method of finding the solution.

d. If possible, determine other related or more general problems for which the techniques will work.

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