Discipuli ordine stantes magistram exspectant, ne sine ordine in scholam intrent.

Ordine is ablative singular of ordo, ordinis (order, row, line).

In ordine stantes, it expresses the way in which the students are standing: in order, in line, in an orderly arrangement. This is often called an ablative of manner or arrangement.

You also see ordine again in sine ordine, but there it is ablative for a different reason: sine (without) takes the ablative.

Stantes is a present active participle of sto, stare (to stand).

It agrees with discipuli in:

• case: nominative
• number: plural
• gender: masculine

So discipuli ordine stantes means the students, standing in line.

A participle is verbal in meaning but adjectival in form: it describes the noun while also carrying an action. So Latin can say in one compact phrase what English often expresses with a clause:

• students standing in line
• or students who are standing in line

Because magistram is the direct object of exspectant.

The verb exspectare means to wait for or to expect, and in Latin it takes a direct object in the accusative. So:

• magistra = nominative singular, the teacher as subject
• magistram = accusative singular, the teacher as object

Here the students are doing the waiting, so discipuli is the subject and magistram is the object.

Exspectant is:

• present tense
• active voice
• indicative mood
• third person plural

It means they are waiting for or they wait for.

It is plural because the subject is discipuli (the students).

Here ne introduces a negative purpose clause.

A purpose clause says what someone does something in order to achieve or avoid something. With a negative purpose, Latin commonly uses ne:

• ut = so that
• ne = so that ... not / lest

So:

• magistram exspectant, ne ... intrent means
• they wait for the teacher so that they do not enter ... or more naturally
• they wait for the teacher lest they enter ...

In this sentence, the idea is that waiting for the teacher prevents disorderly entry.

Because intrent is in the subjunctive, and purpose clauses after ut or ne take the subjunctive in Latin.

So:

• intrant = they enter (indicative, plain statement)
• intrent = that they may enter / lest they enter (subjunctive, in a purpose clause)

More specifically, intrent is:

• present
• active
• subjunctive
• third person plural

The present subjunctive fits well after the present main verb exspectant.

The subject of intrent is still discipuli.

Latin often leaves out a subject when it is already clear from context and from the verb ending. Since intrent is third person plural, and the obvious plural subject in the sentence is discipuli, that is the understood subject.

So the sense is:

• The students wait for the teacher, lest they enter the school without order.

Because in with the accusative usually shows motion into something, while in with the ablative usually shows location in something.

So:

• in scholam = into the school
• in schola = in the school

Since intrent means enter, motion is involved, so Latin uses in + accusative:

• in scholam intrent = enter into the school

They contrast with each other.

• ordine stantes = standing in line / in an orderly way
• sine ordine = without order / not in line / disorderly

The sentence first shows the students already arranged properly, and then gives the reason for waiting: they are waiting for the teacher so that they do not go into the school in a disorderly way.

So the two phrases reinforce the same idea from opposite sides:

• positive arrangement: ordine
• negative possibility to avoid: sine ordine

No. It is a participial phrase, not a full finite clause.

The full main clause is:

• Discipuli ... magistram exspectant = The students wait for the teacher

Then ordine stantes adds extra description about the students:

• the students, standing in line, wait for the teacher

So it works a bit like an English phrase such as:

• The students, standing in line, wait for the teacher.

The sentence is built like this:

• Discipuli = subject
• ordine stantes = participial phrase modifying the subject
• magistram exspectant = main verb and its object
• ne sine ordine in scholam intrent = negative purpose clause

A very literal layout would be:

The students, standing in order, wait for the teacher, lest they enter into the school without order.

More natural English would be something like:

The students, standing in line, wait for the teacher so that they do not enter the school in a disorderly way.

Latin word order is flexible, so the participial phrase can be placed before the main verb for emphasis or smooth flow, without changing the core grammar.