Brutus and TK have pretty much cleared it up, but I just thought I'd note a few things.

Part of the confusion stems from when you consider the Roman Empire to have fallen. The beginning of the MA's is therefore also contested. 476 is the depostion of the last Roman Emperor, but some would argue the Middle Ages had already begun. They might point to the sack of Rome in 410, the Battle of Adrianople in 378 or perhaps even the accession of Constantine in 312 (a religious explanation here: the beginning of the converstion of the empire to Christianity).

Another thing that confuses people is that the first 'Age' of the Middle Ages used to be called the 'Dark Age(s)'. Some older texts will therefore divide things up into the 'Dark Ages' and then the 'Middle Ages'. These are the ones that have the Middle Ages beginning in 800 or 1000.

Scholars generally now divide the Middle Ages into three: The 'Early Middle Ages, from the Fall of Rome to c. 1000, the High Middle Ages, c. 1000-1300, and the Late Middle Ages, c. 1300-1450 or 1500. On top of that, there has also been a strong movement to see the period from the end of Rome to the rise of Charlemagne as its own separate era, 'Late Antiquity', which generally runs from 312 or so up to about 750-800.

Brutus, that division in your schools between the 'age of monks and knights' and the age of states and cities is horrible. 'Knights' themselves didn't appear until about 1000! Ack! I sympathize with you.