Magistra tam clare loquitur ut omnes discipuli intellegant.

It introduces a result clause.

• tam = so
• ut = that

So tam clare loquitur ut ... means she speaks so clearly that ...

This is a very common Latin pattern:

• tam
  • adjective/adverb + ut
• so
  • adjective/adverb + that

Here:

• tam clare = so clearly
• ut omnes discipuli intellegant = that all the students understand

Because it is inside a result clause, and Latin normally uses the subjunctive in result clauses.

So after tam ... ut, you expect a subjunctive verb.

• main clause: Magistra tam clare loquitur
• result clause: ut omnes discipuli intellegant

The subjunctive here does not mean doubt. It is simply the normal grammar for this kind of clause.

It is a result clause, not a purpose clause.

The clue is tam.

• tam clare = so clearly
• that naturally leads to a result: that all the students understand

A purpose clause would mean in order that or so that in the sense of intention.
A result clause means with the result that or so ... that.

Here the sense is not The teacher speaks clearly in order that...
It is The teacher speaks so clearly that...

That makes it a result clause.

Because loquitur comes from loquor, loqui, locutus sum, which is a deponent verb.

Deponent verbs:

• look passive in form
• but have an active meaning

So:

• loquitur looks passive
• but means he/she speaks

This is something English speakers often find strange at first, but it is normal in Latin.

Magistra is nominative singular.

It is the subject of loquitur:

• magistra = the teacher
• loquitur = speaks

So Magistra loquitur = The teacher speaks

Because the verb is third person singular, the singular subject fits perfectly.

It is nominative plural.

Why?

Because omnes discipuli is the subject of intellegant.

• discipuli = students
• omnes = all
• intellegant = understand

So literally:

• all the students understand

Both words match each other:

• omnes = nominative masculine plural
• discipuli = nominative masculine plural

Because omnis must agree with discipuli in case, number, and gender.

Here discipuli is:

• masculine
• plural
• nominative

So omnis becomes:

• omnes

That is the correct nominative masculine plural form.

So:

• omnis discipulus = each/every student or the whole student depending on context
• omnes discipuli = all the students

Because it modifies the verb loquitur, so Latin uses an adverb, not an adjective.

• clara would mean clear in a form agreeing with a noun
• clare means clearly

Compare:

• magistra clara = a clear/famous teacher depending on context
• magistra clare loquitur = the teacher speaks clearly

Since the sentence is describing how she speaks, the adverb clare is needed.

Yes. Latin word order is much more flexible than English word order because the endings show each word’s function.

So these would still mean roughly the same thing:

• Magistra tam clare loquitur ut omnes discipuli intellegant.
• Tam clare magistra loquitur ut omnes discipuli intellegant.
• Ut omnes discipuli intellegant, magistra tam clare loquitur.

However, the original order is very natural and clear:

• subject first: Magistra
• then the degree phrase: tam clare
• then the verb: loquitur
• then the result clause: ut omnes discipuli intellegant

Word order changes often affect emphasis, not basic meaning.

Not in standard Latin for this sentence.

If you have tam ... ut introducing a result clause, the verb in that clause should be subjunctive, so:

• correct: intellegant
• not correct here: intellegunt

If you said intellegunt, it would no longer fit the normal grammar of a result clause.

Intellegant is present subjunctive, third person plural.

It is used because the main verb loquitur is present, and Latin usually follows a sequence of tenses.

Here the main idea is present:

• The teacher speaks

So the result clause also uses a present subjunctive:

• that all the students understand

This keeps the action in the same general time frame.

It comes from intellego, intellegere, intellexi, intellectum = understand.

In this sentence:

• intellegant = they may understand / they understand in a subjunctive result-clause sense

Because it is third person plural, it matches omnes discipuli.

No. Ut can mean several things depending on context.

Common meanings include:

• as
• when
• so that
• that
• in order that

In this sentence, because of tam, it means that in a result sense:

• so clearly that all the students understand

So you should not memorize one single English meaning for ut.
Instead, look at the construction around it.

A very useful clue is the presence of a trigger word like:

• tam = so
• ita = so
• sic = so
• tantus = so great
• tot = so many
• adeo = to such a degree

When you see one of these followed by ut + subjunctive, a result clause is very likely.

So here:

• tam clare = a strong signal
• ut ... intellegant = result clause

A good reading habit is:

1. spot tam
2. expect ut
3. expect a subjunctive
4. translate as so ... that ...

Because the verb ending already shows the person and number.

• loquitur = he/she/it speaks
• the subject magistra tells you specifically that it is the teacher, and therefore she

Latin often leaves out subject pronouns unless they are needed for emphasis.

So Latin does not need to say ea loquitur here.
Magistra loquitur already says everything necessary.

No. In a result clause, Latin normally uses ut non, not ne.

So:

• positive result: ut omnes discipuli intellegant
• negative result: ut omnes discipuli non intellegant

By contrast, purpose clauses usually use:

• ut for positive purpose
• ne for negative purpose

This is a very common distinction:

• purpose: ut / ne
• result: ut / ut non