Mater puero lac purum dat.

Because puero is in the dative case, which is commonly used for the indirect object in Latin.

In this sentence:

• mater = the mother (subject)
• lac purum = pure milk (direct object)
• puero = to/for the boy (indirect object)

So Latin shows the role of puero by its ending -o, instead of using a separate word like to.

Because lac is a neuter noun of the third declension. In Latin, not all direct objects end in -m.

The noun lac, lactis means milk, and its accusative singular is also lac. That is normal for many neuter nouns: their nominative and accusative forms are the same.

So here:

• lac = accusative singular, direct object
• it is what is being given

Because purum is an adjective agreeing with lac.

Latin adjectives must agree with the nouns they describe in:

• gender
• number
• case

Here, lac is:

• neuter
• singular
• accusative

So the adjective must also be:

• neuter
• singular
• accusative

That is why we get purum: lac purum = pure milk.

Dat is:

• third person singular
• present tense
• active voice
• indicative mood

It comes from the verb dare, meaning to give.

So dat means he/she/it gives.
In this sentence, because the subject is mater, it means the mother gives.

We know because mater is in the nominative case, which is the usual case for the subject of a sentence.

Also, dat is singular, and mater is a singular noun, so they match naturally:

• mater = the mother
• dat = gives

So mater is the one doing the action.

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

So:

• mater can mean mother, a mother, or the mother
• puero can mean to a boy or to the boy
• lac can mean milk, some milk, or the milk

English has to choose an article when translating, but Latin usually does not state it explicitly.

Latin word order is much more flexible than English word order because Latin uses endings to show each word’s role.

English depends heavily on order:

• The mother gives the boy pure milk

Latin can move words around more freely because the cases tell you what each word is doing.

So Mater puero lac purum dat is natural Latin, especially with the verb dat at the end, which is very common.

Yes, often it could.

For example, these would still mean essentially the same thing:

• Mater puero lac purum dat
• Puero mater lac purum dat
• Lac purum mater puero dat
• Mater lac purum puero dat

The endings still show:

• mater = subject
• puero = indirect object
• lac purum = direct object

However, changing the order can slightly change the emphasis or style.

Because the verb dare often takes two objects in sense:

• the thing given
• the person receiving it

In Latin, the thing given is usually in the accusative and the recipient is usually in the dative.

So here:

• lac = the thing being given = direct object
• puero = the recipient = indirect object

You would usually look them up like this:

• mater, matris = mother
• puer, pueri = boy
• lac, lactis = milk
• purus, pura, purum = pure
• do, dare, dedi, datum = give

These dictionary forms help you identify the declension or conjugation and understand why the words appear in these sentence forms.

Because Latin verb endings already tell you the person and number.

The ending in dat tells you the subject is:

• third person
• singular

So Latin does not need to add a separate pronoun like she unless it wants extra emphasis.

That means mater dat already clearly means the mother gives.

No. Mater is a third-declension noun, not a first-declension noun.

A learner might expect many feminine nouns to be first declension, but grammatical gender and declension are not the same thing.

So:

• mater is feminine
• but it belongs to the third declension

Its forms include:

• nominative singular: mater
• genitive singular: matris

That is why it does not look like a typical first-declension noun such as puella.