### Multiple variables in an equation

OBJECTIVE: To understand and use the fundamental problem-solving element, Request-Response-Result, when more than one variable is present in an equation.
In processing an equation, work from left to right through the equation, dealing with each quantity requested in the order in which they are encountered.

Response to the individual requests are all indented to the same indent level. Each indentation is one indent step to the right of the indentation of the requesting equation.

Responses to the individual requests made by an equation are frequently in the problem statement.

The answer to the above problem can be obtained instantly by the in-the-head method. In using the in-the-head method all of the steps shown above are actually done. Think about it! By using the in-the-head method on simple problems the student loses the opportunity to learn how to solve problems. Problems quickly become sufficiently complex that the in-the-head method does not work. The working memory is simply not adequate to handle the steps of such problems. This has nothing to do with intelligence. It is just the way our brains are built.
The multiple variables present in an equation can be connected in a great variety of ways using the common mathematical operations of addition, multiplication, subtraction, division and exponentiation.

The following example shows the use of multiplication to connect two variables.

In equations containing more than one variable, some of the variables may be related in some manner specified by the problem statement. This situation is quite common. The following example illustrates this for a particular case.

Even quite simple problems can contain enough data to exceed the capacity of the working memory and the in-the-head method fails. The following problem is such an example. Yet the solution process is precisely the same as that used in the previous 3 examples. Simply responding in order to the requests made by the starting equation generates the solution. Problems are self-solving.

Have your students construct problems which have the characteristics of these examples. Their problems will have the same solution structure as that shown in these examples. Also examine textbooks and other instructional materials for problems which have the solution structure shown here.

In the examples on this page a concept, a principle or definition, was used to start each solution.

The words change, the numbers change and the concepts change but the problem-solving process remains the same.