Discipula magistrae gratias agit, quod hanc sententiam alio modo explicavit.

Because gratias agere means to give thanks or to thank, and the person being thanked is put in the dative.

So:

• magistra = teacher as a subject
• magistrae = to the teacher

In this sentence, Discipula magistrae gratias agit literally means The student gives thanks to the teacher, which is the normal Latin way to say The student thanks the teacher.

Gratias agere is an idiomatic Latin expression.

• gratias is the accusative plural of gratia
• agit means does, drives, or in this expression gives/offers

Together, gratias agere means to give thanks.

This is similar to how English often uses a phrase rather than a single word, as in to give thanks. Even though English usually says thank, Latin very commonly says gratias agere.

So:

• gratias agit = she gives thanks = she thanks

In Latin, the expression is normally gratias agere, with gratias in the plural. This is just the standard idiom.

You do not need to translate the plural very literally. It does not usually mean several thanks in a special way; it is simply how Latin says thanks.

This is similar to English expressions like thanks or congratulations, which are plural in form even when the meaning is singular or general.

Here quod means because.

It introduces the reason why the student thanks the teacher:

• Discipula magistrae gratias agit = The student thanks the teacher
• quod hanc sententiam alio modo explicavit = because she explained this sentence in another way

So quod is functioning as a conjunction, not as a relative pronoun.

A learner may first know quod as which or because, so context matters. Here it clearly means because.

Because it is the direct object of explicavit.

The verb explicare means to explain. What did she explain?

• hanc sententiam = this sentence

Both words are accusative singular feminine:

• hanc = accusative singular feminine of hic, haec, hoc
• sententiam = accusative singular of sententia

They match because hanc describes sententiam.

Hanc means this and points to sententiam.

It is the feminine accusative singular form of hic, haec, hoc, because:

• sententia is feminine
• it is singular
• it is the direct object of explicavit, so it must be accusative

So:

• haec sententia = this sentence as a subject
• hanc sententiam = this sentence as an object

This is a good example of how Latin demonstratives change form to match the noun they describe.

Alio modo means in another way or by another method.

Both words are in the ablative singular:

• alio = ablative singular of alius
• modo = ablative singular of modus

This is an example of the ablative of manner or a closely related idiomatic use. Latin often uses the ablative to express the way in which something is done.

So:

• alio modo explicavit = she explained it in another way

It is worth learning this as a common phrase:

• eo modo = in that way
• hoc modo = in this way
• alio modo = in another way

It most naturally refers to the teacher.

The sentence says:

• The student thanks the teacher
• because she explained this sentence in another way

The person who did the explaining is the reason for the thanks, so logically it is the teacher.

Latin often leaves subject pronouns unstated, because the verb ending already tells you the person and number:

• explicavit = he/she/it explained

Since both discipula and magistra are feminine singular nouns, English has some ambiguity if you look only at grammar. But the meaning and context make the teacher the natural subject of explicavit.

Explicavit is the perfect active indicative of explicare.

Here it means explained. The perfect tense is used because the explanation is presented as a completed action.

So the idea is:

• first, the teacher explained the sentence
• as a result, the student thanks her

Latin often uses the perfect for a single completed past action, just as English uses the simple past.

Because the two actions happen at different times.

• agit = is thanking / thanks now, in the main statement
• explicavit = explained earlier, giving the reason

So the sequence is very natural:

1. the teacher explained the sentence
2. now the student thanks her for that

Latin does not need to force the two verbs into the same tense. Each verb simply shows its own time in relation to the situation being described.

Yes, but it is also very normal Latin word order.

The sentence is:

Discipula magistrae gratias agit, quod hanc sententiam alio modo explicavit.

A few things to notice:

• Discipula comes first, giving the subject immediately
• magistrae comes before gratias agit, so the recipient of the thanks is introduced early
• gratias agit stays together as a set expression
• in the subordinate clause, hanc sententiam comes before explicavit, which is very common in Latin
• the verb explicavit comes at the end of its clause, a very typical Latin pattern

Latin word order is more flexible than English because case endings show grammatical function. But this sentence still feels quite natural and straightforward.

Yes, in many contexts quia and quod can both mean because.

However, quod is very common for introducing a clause that gives the reason for an emotion or action, especially after verbs like:

• gaudeo = I rejoice
• doleo = I am sorry
• gratias ago = I give thanks

So gratias agit, quod... is a very natural Latin pattern:

• she thanks her because...

A learner should recognize that both quod and quia can introduce causal clauses, but here quod is especially idiomatic.

Here are the main forms:

• discipula from discipula, discipulae = female student
• magistrae from magistra, magistrae = female teacher
• gratias from gratia, gratiae = favor, gratitude, thanks
• agit from ago, agere, egi, actum = do, drive, act
• quod can be a conjunction meaning because
• hanc from hic, haec, hoc = this
• sententiam from sententia, sententiae = sentence, opinion, thought
• alio from alius, alia, aliud = other, another
• modo from modus, modi = way, manner, method
• explicavit from explico, explicare, explicavi, explicatum = explain

Looking up full dictionary forms is especially useful in Latin because the sentence often shows only one inflected form.