For instance, the verb conjugations in English provide a hard and obvious distinction between countables and uncountables:
- Some ____ is good.
- Some ____ are good.
Here's your prompt
How many words are in this piece of text?
(And you have a paragraph or a page of text to hand.)
You could answer that as how many unique words or as the word processor does, recounting duplicates as often as they appear. Linguists call the first the number of "types" and the second the number of "tokens". The students understand the concepts, so just stick the labels on and be done.
Is "wants" a different word from "want"? And "wanted"?
The two concepts here are "word-forms" (you can say "wants" is a different word-form from "want" without claiming it's a different "word") and "lemmas" (the set of all variants of a single dictionary headword).
The English speaker already understands "want, wants, wanted" as a set -- we're just calling that set a "lemma". The English speaker already understands "cat, cats" as a set -- again, we're just slapping the label "lemma" on a known and understood concept.
Of course, you're all crying out that types, tokens, word-forms and lemmas are of no practical use in the language class, and you're probably right. It just so happens that I'm quite lazy, and rather than give dozens of examples of differing complexity, I wanted to skip from "simple" to "complex" in a single bound in order to demonstrate that even the most seemingly abstract linguistic ideas are readily available to the beginner. If the easiest questions can be addressed this way, and the most difficult ones can too, you can be confident that most things in between can be handled in the same manner.
The other very important thing to take out of the question "what is a word?" is that the human brain doesn't run on fixed rules. The human brain has a set of fuzzy rules that interact and make our own reality. We internally maintain innumerable unresolved paradoxes and contradictions, and yet the end result is still functional and useful. But each of these contradictions can be broken apart, and we only need one of them to teach a new concept -- one concept, "the word", gave us four distinct concepts: token, type, word-form and lemma.
So when we're taking a native-language concept and trying to use it to teach a slightly different target-language concept, we don't need to carry over the full thing -- keep the bits that work, ditch the things that don't. We don't need a full and precise rule -- the brain doesn't like them anyway.