Mascara, armpit farts, and French films

We're making progress in our conversation about Latin, nouns, and irresponsible sample sentences.  Let me recap what we know so far:  the idea of case explains how nouns have different possible roles in a sentence and those roles are called by the (so far) specific names nominative (subject) and accusative (direct object).  We've been reading a lot, writing some, and are willing to talk about it in polite company.
As we've read we noticed that nouns seem to hang about together like friends at a dance, whispering to each other and giving knowing looks.  Via, mensa, villam, and Metella are huddled up talking about shoes and eyeliner.  Every so often they giggle and look across the dance floor.  They see servus, hortus, venalicius, the the shifty Caecilius engaged in armpit farts and lots of sports talk.   Atrium, cubiculum, and triclinium are close by the boys, though the girls can't quite figure out why.  And walking into the cafeteria come canis, mercator, pictor, their jolly leader Grumio talking loudly about art and cuisine, literature and French films.
So what is going on here?  Our readings reveal that nouns group together and their groups fall in line with how they express their cases.  Nouns like via--let's call them the sisters--all share -am when made direct objects.  And those like servus--the brothers--likewise share -um as direct objects (as do those oddballs like cubiculum, but they definitely aren't quite the same).  Finally, Grumio and his crew--we'll call them something clever later--use -em.
Now Latin calls these three groups something much more boring--the first, second, and third declensions respectively.  Yet we are wise to note what is going on here.  The change is not random, and if you know ahead of time the group--the declension--a noun belongs with, you will not struggle to catch what the Latin is telling you.  This is because every noun in its group uses the same endings to get across its roles.
So as we read, pay attention to the nouns.  Mark who they hang with.  You will begin to see the cliques.  If you're lucky, you may even be asked to slow-dance.