Puer lapillum in via invenit et matri ostendit.

Latin has no articles. It does not have separate words for the, a, or an.

So:

• puer can mean the boy or a boy
• lapillum can mean the pebble or a pebble
• via can mean the road or a road

English has to add an article, but Latin usually leaves that to context.

Puer is the subject of the sentence, so it is in the nominative singular.

Its dictionary form is puer, pueri, meaning boy.
Because it is a second-declension masculine noun, the nominative singular is simply puer.

If it were a direct object instead, you would expect puerum.

Because lapillum is the direct object of invenit: it is the thing the boy finds.

• dictionary form: lapillus
• accusative singular: lapillum

So:

• lapillus = a/the pebble as subject
• lapillum = a/the pebble as direct object

Also, lapillus is a diminutive form, so it means small stone or pebble.

Because in takes different cases depending on the meaning:

• in + ablative = in/on a place, showing location
• in + accusative = into/onto a place, showing movement toward

Here the pebble is being found in/on the road, so this is location, not motion. That is why Latin uses the ablative:

• in via = in/on the road

If someone were walking into the road, Latin would use in viam instead.

It is ablative because it follows in in the sense of location.

The dictionary form is via, viae.
Its ablative singular is via.

So in in via, the form via is not nominative here; it is ablative singular.

Matri is the dative singular of mater, matris, meaning mother.

The dative case is often used for the indirect object:

• the person to whom something is shown, given, said, etc.

So:

• matri ostendit = he showed [it] to his mother

This is the same basic idea as English to his mother.

Latin often leaves out possessive words like his, her, or their when the relationship is obvious from context, especially with family members.

So matri can naturally be understood as to his mother here.

If Latin wanted to make it explicit, it could say matri suae, but that is not necessary in a sentence like this.

Because the object is understood from the previous part of the sentence.

The boy finds lapillum, and then he shows [it] to his mother. Latin often omits a repeated object when it is obvious.

So:

• Puer lapillum in via invenit et matri ostendit means
• The boy found a pebble in the road and showed it to his mother

Latin could add a pronoun, but it does not need to.

Both forms are third-person singular, so they mean he/she/it finds/shows or he/she/it found/showed, depending on context.

This is a point that often confuses learners:

• invenit can be present or perfect in spelling without macrons
• ostendit can also be present or perfect in form

So the correct tense comes from context or from the meaning already supplied in your exercise.

If your translation is past, then read them as:

• he found
• he showed

If your translation is present, then read them as:

• he finds
• he shows

Because Latin does not need to repeat the subject if it stays the same.

The ending -t in ostendit already tells you the verb is third-person singular. Since puer has already been given as the subject, Latin simply continues with the same subject:

• The boy finds ... and shows ...

English also often does this:

• The boy found a pebble and showed it to his mother

The word order matters less in Latin than in English because the case endings show the grammatical roles.

So Latin can move words around more freely:

• puer is the subject because it is nominative
• lapillum is the direct object because it is accusative
• matri is the indirect object because it is dative
• via is ablative after in

This means the sentence could be rearranged in other ways without changing the basic meaning. The order here is a normal, natural one, but not the only possible one.