There are two related standards:

6.EE.6. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

and

6.EE.7. Solve real-world and mathematical problems by writing and solving equations of the form $x+p=q$ and $px=q$ for cases in which $p$, $q$ and $x$ are all nonnegative rational numbers.

Both of these occur the margin in the passage you mention in the Progression. The first is about variables and expressions, the second is about equations. Since expressions are used in writing equations, the reference to a “set” in 6.EE.6 could refer to a solution set in the context of 6.EE.7, but it does not have to. The Progression illustrates this with the example of the expression $0.44n$ to represent the price in dollars of $n$ stamps: here $n$ comes from the set of whole numbers. And note that 6.EE.6 does not refer to a “set of solutions” but rather simply to a “set.”

As to your last question, it is certainly true that in many instances where one uses a variable to stand for a single unknown, it will be in the context of writing an equation to find that unknown. That is, the use of variables described in 6.EE.6 to represent an unknown number will arise in the practice described in 6.EE.7 of writing equations to solve problems. There is indeed a close connection between the two standards. Still, it seems worth distinguishing the idea of choosing a letter to represent an unknown number as an important idea in its own right.

• This reply was modified 10 years, 8 months ago by Bill McCallum.