Post concentum convivae magistrae gratias agunt.

Because post is a preposition that regularly takes the accusative case in Latin when it means after.

So:

• post = after
• concentum = accusative singular

That gives post concentum = after the song / after the performance / after the concert, depending on the context.

Concentum is the accusative singular of concentus, -us (a 4th-declension noun).

A learner might expect a 2nd-declension ending because -um often looks familiar from words like servum, but here it belongs to a 4th-declension noun:

• nominative singular: concentus
• accusative singular: concentum

So after post, Latin uses the accusative form concentum.

The main clue is the verb agunt, which is 3rd person plural: they do / they give / they offer.

That means the subject must be plural. Convivae can be several things morphologically, but here the most natural one is:

• convivae = nominative plural = the guests

So:

• convivae = subject
• agunt = they give / they render

Together: the guests give thanks.

Yes. Like many 1st-declension forms, convivae is potentially ambiguous. It could be:

• nominative plural
• genitive singular
• dative singular
• vocative plural

But in this sentence, nominative plural is the only reading that fits naturally, because:

• the verb agunt is plural
• the sentence needs a clear plural subject
• convivae works perfectly as the guests

So Latin form ambiguity is normal; the syntax usually tells you which meaning is right.

Because the sentence already has a good subject in convivae, and gratias agere normally takes the person thanked in the dative.

So here:

• convivae = nominative plural, the guests
• magistrae = dative singular, to the teacher

That gives:

• gratias agere alicui = to give thanks to someone

So magistrae is not the teachers here; it is to the teacher.

By form alone, yes. Magistrae could be:

• genitive singular = of the teacher
• dative singular = to/for the teacher
• nominative plural = the teachers
• vocative plural = O teachers

But in this sentence, the idiom gratias agere strongly points to a dative:

• gratias agere magistrae = to give thanks to the teacher

So context and idiom settle the meaning.

Literally, gratias agunt means something like they give thanks or they express thanks.

It is a standard Latin idiom:

• gratia can mean favor, thanks, gratitude
• gratias agere = to give thanks / thank

English uses a simple verb, to thank, but Latin often expresses the same idea with a noun + verb phrase. This is very common in Latin.

Because the idiom is normally gratias agere, with gratias in the accusative plural.

Even though English says thanks or gratitude in different ways, Latin conventionally uses the plural here. So learners should treat it as a set expression:

• gratias ago = I thank / I give thanks
• gratias agis = you thank
• gratias agit = he/she thanks
• gratias agunt = they thank

It is best learned as a whole phrase rather than translated word-by-word every time.

Agunt is present active indicative, 3rd person plural, from ago, agere.

So it means:

• they do
• they drive
• they act
• in this idiom, they give thanks / they thank

In this sentence, the most natural translation is the guests thank the teacher or the guests give thanks to the teacher.

Latin word order is more flexible because case endings show each word’s function.

English depends heavily on position:

• The guests thank the teacher

Latin can move the words around more freely because the endings identify the relationships:

• convivae = subject
• magistrae = indirect object / person thanked
• gratias = object within the idiom
• agunt = verb

So Post concentum convivae magistrae gratias agunt is perfectly normal Latin word order, even though a very literal English ordering would sound unusual.

Because Classical Latin has no articles like English the or a/an.

So:

• convivae can mean guests or the guests
• magistrae can mean to a teacher or to the teacher
• concentum can mean a performance or the performance

Which one is best in English depends on context. The Latin itself does not mark that distinction directly.

It attaches to the event of the sentence as a whole. It tells you when the action happens:

• Post concentum = after the performance / after the singing
• then the main action happens: the guests thank the teacher

So it functions as a time expression modifying the whole clause, not just a single noun.