## Problem Solving Strategies

### Understand

1. Read the problem carefully.

2. Make sure you understand the situation that is described.

3. Make sure you understand what information is provided, and what the question is asking.

4. For many problems, drawing a clearly labeled picture is very helpful.

### Plan

1. First focus on the objective. What do you need to know in order to answer the question?

2. Then look at the given information. How can you use that information to get what you need to know to answer the question?

3. If you do not see a clear logical path leading from the given information to the solution, just try *something*. Look at the given information and think about what you can find from it, even if it is not what the question is asking for. Often you will find another piece of information that you can then use to answer the question.

### Write equations

You need to express mathematically the logical connections between the given information and the answer you are seeking. This involves:

1. Assigning variable names to the unknown quantities. The letter *x* is always popular, but it is a good idea to use something that reminds you what it represents, such as *d* for distance or *t* for time. The trickiest part of assigning variables is that you want to use a minimum number of different variables (just one if possible). If you know how two quantities are related, then you can express them both with just one variable. For example, if Jim is two years older than John is, you might let *x* stand for John’s age and (*x* + 2) stand for Jim’s age.

2. Translate English into Math. Mathematics is a language, one that is particularly well suited to describing logical relationships. English, on the other hand, is much less precise. The next page is a table of English phrases and theircorresponding mathematical meanings, but don’t take it too literally. The meaning of English words has to be taken in context.

### Solve

Now you just have to solve the equation(s) for the unknown(s). Remember to answer the question that the problem asks.

### Check

Think about your answer. Does your answer come out in the correct units? Is it reasonable? If you made a mistake somewhere, chances are your answer will not just be a little bit off, but will be completely ridiculous