Singular and plural

The Finnish approach to singular and plural objects of sentences is a bit complicated. In English if I said something along the lines of "would you like the fish", "would you like some fish?" or "would you like a fish?" or "would you like fish?" you would know what I mean without having to think. Of course it's the same for native Finnish speakers offering each other fish, but they don't have the definite and indefinite article, for starters and ... well, lets dive in and learn by example.

Would you like is haluatko in Finnish, and fish is kala.

First case: would you like some (part of this one) fish
haluatko kalaa

There is an extra a on the end of kala because it's in the singular partitive. You're offering part of one fish. In English we would just say "some fish."

Second case: would you like a (single non-specific) fish
haluatko kalaa

Again, the extra a because it's the singular partive. You're offering one of many non-specific fish. In English we'd say "a fish" or perhaps "fish."

Third case: would you like the fish (a specific fish)
haluatko kalan

Suddenly kala is in the genetive case by adding an n - which means "of the fish". So you're asking "would you like of the fish." Yep, doesn't make much sense in English, but it's how you offer someone a specific single fish.

Fourth case: would you like the fish (a specific number, each fish identified)
haluatko kalat

Fish is put in the nominative plural. This is a rather contrived situation so it's rare. You'd have to be in a situation where someone had selected, say, three specific Japanese fighting fish and you were holding them for him. Then when he came round to visit you'd be asking him if he would like the fish (a specific number, each fish known).

Fifth case: would you like some (of many) fish
haluatko kaloja

In this example fish is in the partitive plural. Initially this didn't make much sense to me, and in speech a Finn is probably actually going to use the partitive singular. So this is the case where they're serving whitebait, for example, and your as the host ask a guest if she would like some fish.

But cheer up. A Finn asking you if you would like some of many fish is probably going to say: "would you like some fishes?"

And then you get to correct them.