From David Wees: what do we mean by variable?
I see this as one of the huge barriers to high school math as middle schools transition from arithmetic to algebra–see Hung-Hsi Wu with a stellar presentation on these challenges.
Wu’s answer, which I like, is that, in K-5, math is about arithmetic–calculating and manipulating numbers. In 9-12, math is about algebra–learning what is true in general, for all numbers. This is oversimplified, but gets at the main difference. In 6-8, this transition needs to focus on what it means for a variable to represent numbers in general–this goes beyond memorizing what like terms are, or solving one-step equations. It means reasoning, and explaining that reasoning, in a question about generalities–solving a problem for one instance of a variable, then solving it again for a different instance of the variable. This is what algebra is actually use for, at a basic level (it’s why people don’t actually use math in the workplace–someone write a formula or creates a table, and does the math for the worker).