What Does a Math Teacher Mean When She Says, "Write a Verbal Expression to Represent Each Expression"?

When a math teacher says, "Write a verbal expression to represent each expression," she wants the students to change the algebraic representation into English sentences. Algebra can be denoted by sentences formed of specific English terms that indicate the use of a mathematical operator.

For example, if an algebraic expression "3x + 5 = 20" is given, the verbal expression of such an expression can be written, "Find a number such that 5 added to 3 times the number gives 20," or it can also be written, "Find a number that yields 20 when 5 is added to 3 multiplied by that number."

While writing the verbal expressions, it is very important to write in such a way that obtaining the algebraic expression back from it does not become a tedious task. Knowing how to write algebraic expressions from verbal expressions – and writing verbal expressions from algebraic equations – is important, because variables clearly indicated as "x" or "y" generally do not exist in problems that must be solved in day-to-day life. Instead, one must deal with English words that describe the same concepts as certain mathematical operations. For instance, no one is likely to say say, "Solve 3x + 5 = 20" in a typical job. Instead, the problem may arise in terms of finding the number of cars that must be produced so that five cars added to thrice that number results in a total of 20 cars.