Mater puero viam ad forum monstrat.

Because mater is in the nominative case, which is the case normally used for the subject of the sentence.

Here, mater means mother and is the one doing the action of showing.

A learner might expect a special ending for the subject, but mater is a third-declension noun, so its nominative singular form is simply mater.

Because monstrare can take two objects in Latin:

• the thing shown
• the person to whom it is shown

In this sentence:

• viam = the thing being shown
• puero = the person to/for whom it is shown

So puero is in the dative case, which often expresses to or for someone.

That is why Latin uses:

• puero = to the boy not
• puerum = the boy as a direct object

Because viam is the direct object: it is the thing that is being shown.

The verb monstrat means shows, and the question shows what? is answered by viam.

• via = road, way
• viam = road/way as a direct object

So the accusative marks the thing directly affected by the action.

Because some verbs naturally involve:

• a direct object in the accusative
• an indirect object in the dative

With monstrare, this is very common:

• aliquid alicui monstrare = to show something to someone

So in this sentence:

• viam = something
• puero = to someone

This is similar to English Mother shows the way to the boy, though English often prefers shows the boy the way.

Because ad means to or toward, and it is used with the accusative to show motion toward a place.

So:

• ad forum = to the forum

Without the preposition, forum by itself would not naturally express that same idea here.

This phrase modifies viam: it is the road to the forum.

Because the preposition ad takes the accusative case.

So:

• ad + accusative = to, toward

That gives:

• forum as the accusative form of forum

This is not because forum is the direct object of monstrat.
The direct object is viam.
Forum is accusative because it belongs to the prepositional phrase ad forum.

Most naturally, it describes viam.

So the sense is:

• the road to the forum

rather than:

• Mother shows the road, toward the forum

In other words, ad forum tells us what kind of road/way it is.

So the structure is best understood as:

• Mater = subject
• puero = indirect object
• viam ad forum = direct object phrase
• monstrat = verb

Latin often places the verb near the end of the sentence, especially in straightforward prose. This is a very common Latin word order pattern.

However, Latin word order is more flexible than English word order because the cases show each word’s function.

So even if the words were rearranged, the meaning could remain basically the same, for example:

• Mater viam ad forum puero monstrat
• Puero mater viam ad forum monstrat

The endings tell you who is doing what to whom.

Yes. That is a very natural English translation.

Latin has:

• puero = to the boy
• viam = the way
• ad forum = to the forum

English often turns the dative idea into a double-object construction:

• shows the boy the way

So both of these reflect the Latin well:

• The mother shows the way to the forum to the boy
• The mother shows the boy the way to the forum

The second is more natural English.

Monstrat is present tense, third person singular, active voice.

That means:

• he/she/it shows

Since the subject is mater, it means:

• mother shows

It comes from the verb monstrare, meaning to show.

Because mater is the singular nominative form.

The plural would be:

• matres = mothers

Also, the verb is singular:

• monstrat = shows not
• monstrant = show

So both the noun and the verb tell us the subject is singular.

They come from different declensions:

• mater, matris = third declension
• puer, pueri = second declension
• via, viae = first declension
• forum, fori = second declension neuter

That is why the endings are different:

• mater stays mater in the nominative singular
• puero has the dative singular ending of a second-declension masculine noun
• viam has the accusative singular ending of a first-declension noun
• forum is accusative singular neuter after ad

It can mean either, depending on context.

In this sentence, viam ad forum could be understood as:

• the road to the forum
• the way to the forum

In beginner translations, way is often smoother in English, but road is also perfectly possible depending on the situation.