Post balneum pueri in palaestra ludere volunt, sed magistra dicit eos adhuc fessos esse.

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

• post = after
• balneum = bath, bathing, bathhouse (accusative singular)

So post balneum means after the bath or more naturally after bathing.

It can mean either, depending on context.

In a sentence like this, post balneum often means something like:

• after the bath
• after bathing
• after going to the baths

Latin often uses a concrete noun where English might use a more abstract phrase. So even if the literal wording is after the bath, the natural sense may simply be after bathing.

Because pueri is the subject of volunt.

The main clause is:

• pueri ... volunt = the boys want ...

So pueri must be in the nominative plural.

Here is the basic structure:

• pueri = the boys
• ludere = to play
• volunt = want

Together: the boys want to play

Because in can take either the ablative or the accusative, depending on meaning.

• in + ablative = in / on (location)
• in + accusative = into / onto (motion toward)

Here, in palaestra means in the wrestling school / in the gym / in the exercise yard as a location, not motion into it.

So:

• in palaestra = in the palestra
• in palaestram would mean into the palestra

A palaestra is a Greek-style exercise ground or wrestling school. In school Latin, it is often translated simply as:

• gym
• exercise yard
• wrestling school

So in palaestra ludere means something like to play in the gym/exercise yard.

Because it depends on volunt.

In Latin, verbs like volo (I want) are commonly followed by an infinitive, just like in English:

• volo ludere = I want to play
• pueri ludere volunt = the boys want to play

So ludere is a complementary infinitive: it completes the meaning of volunt.

Because this is the normal Latin way to express want to do something.

Latin usually uses:

• volo + infinitive = want to ...

Examples:

• venire volo = I want to come
• legere volunt = they want to read
• ludere volunt = they want to play

This is very similar to English.

Because after verbs like dicit (says), Latin often uses an indirect statement, also called an accusative-and-infinitive construction.

Instead of saying something like the teacher says that they are still tired with a separate clause introduced by that, Latin usually says:

• magistra dicit = the teacher says
• eos = them
• fessos esse = to be tired

Literally, this is something like:

• the teacher says them to be still tired

But in natural English:

• the teacher says that they are still tired

Because in an indirect statement, the subject of the infinitive goes into the accusative.

Here, the boys are the understood subject of esse:

• eos ... esse = that they are ...

So Latin uses:

• eos = accusative plural masculine of is, ea, id

It is not ei, because ei would be nominative plural (they) or dative singular/plural in other contexts, and that is not what the indirect statement requires.

Because fessos agrees with eos.

In the indirect statement:

• eos = them (accusative plural masculine)
• fessos = tired (accusative plural masculine)
• esse = to be

Latin adjectives agree with the nouns or pronouns they describe in gender, number, and case. Since eos refers to the boys, fessos must also be:

• masculine
• plural
• accusative

Here adhuc means still.

So:

• eos adhuc fessos esse = that they are still tired

Depending on context, adhuc can also mean up to this point or so far, but still is the most natural meaning here.

Yes, Latin can sometimes omit esse, especially when the meaning is clear. But including it is completely normal and often clearer, especially for learners.

So both of these can occur:

• dicit eos fessos esse
• dicit eos fessos

Both can mean she says that they are tired, but the version with esse is fuller and more explicit.

Latin word order is much more flexible than English word order because Latin shows grammatical relationships through endings, not mainly through position.

English depends heavily on order:

• The boys want to play

Latin can move words around more freely because:

• pueri shows the subject
• volunt shows the main verb
• eos shows the accusative subject of the indirect statement
• fessos agrees with eos

So this sentence could be rearranged in several ways and still mean the same thing, though the emphasis might change.

The given order is quite natural:

• time phrase first: Post balneum
• main subject and action: pueri ... ludere volunt
• contrast: sed
• new subject and reported statement: magistra dicit eos adhuc fessos esse

Because Classical Latin has no articles.

Latin does not have direct equivalents of English the and a/an. Whether a noun is definite or indefinite is understood from context.

So:

• pueri can mean the boys
• magistra can mean the teacher
• palaestra can mean the gym/exercise yard

English must choose an article, but Latin usually does not state one.