Lucia post lectionem cum magistra locuta est, et magistra novum verbum in tabula inscripsit.

Because post takes the accusative.

So post lectionem means after the lesson, and lectionem is accusative singular of lectio.

This is a very common pattern:

• post cenam = after dinner
• post bellum = after the war

Because the preposition cum takes the ablative when it means with.

So:

• cum magistra = with the teacher

Even though magistra looks the same as the nominative singular, here its role is shown by the preposition cum.

It is the same word form, but it has two different grammatical jobs:

1. In cum magistra, it is ablative singular after cum
2. In et magistra novum verbum..., it is nominative singular, the subject of inscripsit

This happens because for many first-declension nouns, the nominative singular and ablative singular both end in -a.

So you have to tell the case from the context, not just the ending.

Because loquor is a deponent verb.

A deponent verb:

• has passive-looking forms
• but an active meaning

The perfect tense of loquor is formed with:

• a perfect participle: locuta
• a form of sum: est

So locuta est means she spoke or she has spoken, not she was spoken.

The dictionary form is:

• loquor, loqui, locutus sum = to speak

Because the subject is Lucia, who is feminine.

The participle in a deponent perfect must agree with the subject:

• locutus est = he spoke
• locuta est = she spoke
• locuti sunt = they spoke, masculine or mixed
• locutae sunt = they spoke, feminine

So locuta matches Lucia.

Because the two verbs belong to different types.

locuta est

This is a deponent perfect, which is built with:

• participle + sum

inscripsit

This is a regular active perfect, expressed in one word.

So both verbs are in the perfect tense, but they are formed differently:

• locuta est = she spoke
• inscripsit = she wrote/inscribed

Both are perfect tense.

In a sentence like this, the Latin perfect usually describes a completed action in the past:

• locuta est = she spoke
• inscripsit = she wrote

In natural English, this often becomes the simple past.

So the sentence narrates two completed actions:

1. Lucia spoke with the teacher after the lesson
2. the teacher wrote a new word on the board

Because verbum is neuter.

The adjective novus, nova, novum must agree with verbum in:

• gender
• number
• case

Since verbum is:

• neuter
• singular
• accusative here

the adjective must also be:

• neuter
• singular
• accusative

So:

• novum verbum = a new word

Because it is the direct object of inscripsit.

The teacher is the one doing the action, and the thing written is the new word.

So:

• magistra = subject
• novum verbum = direct object

That is why verbum is in the accusative.

Because Latin in + ablative can be used for location, and with surfaces it is often translated into English as on.

So in tabula literally looks like in/on the board, but in good English the natural translation is often on the board.

Also, tabula can mean several things depending on context, such as:

• board
• tablet
• writing tablet
• plank

Here board makes sense.

Because in takes the ablative when it means in or on in the sense of location.

Compare:

• in tabula = on the board, in the board area, located there
• in tabulam = into the board / onto the board, with motion toward it

Here the word is being written on the board, so Latin uses in tabula.

Latin often repeats a noun when it wants to be clear about the subject, especially when the subject changes or when clarity matters.

Here the first subject is Lucia, and the second subject is magistra. Repeating magistra makes that shift very clear.

Latin could sometimes omit a subject pronoun, but repeating the noun is completely normal and often stylistically helpful.

Latin word order is much more flexible than English word order because the endings show the grammatical roles.

So this sentence could be rearranged in other ways and still mean the same thing, as long as the forms stay the same.

For example, the core relationships are clear because of the cases and verb forms:

• Lucia = subject of locuta est
• lectionem = object of post
• magistra after cum = ablative
• magistra later = subject of inscripsit
• novum verbum = object of inscripsit
• tabula = ablative after in

The given order is natural and readable, but not the only possible order.