November frigidior est quam October, et pueri domi libentius manent.

Because frigidior is the comparative form of frigidus.

• frigidus = cold
• frigidior = colder

The sentence is comparing November with October, so Latin uses the comparative adjective, just as English uses colder instead of cold.

Also, frigidior is nominative singular masculine here, agreeing with November.

It is formed from the adjective stem of frigidus plus the comparative ending -ior.

A helpful pattern is:

• masculine/feminine nominative singular: -ior
• neuter nominative singular: -ius

So:

• frigidior = colder, for masculine or feminine
• frigidius = colder, for neuter

Even if the basic adjective is a first/second-declension adjective like frigidus, its comparative is declined as a third-declension adjective.

Because after quam, Latin often puts the thing compared in the same case as the word it is being compared with.

Here, November is nominative, so October is also nominative:

• November frigidior est quam October

That is the normal than October construction.

Latin also has another way to say this without quam:

• November Octobri frigidior est

There, Octobri is ablative. Both constructions are correct.

No. It agrees only with November.

In this sentence, November is the subject, and frigidior describes it:

• November = the thing being described
• October = the standard of comparison

So frigidior is singular because November is singular.

Because each verb agrees with its own subject.

• November frigidior est: November is singular, so est is singular.
• pueri domi libentius manent: pueri is plural, so manent is plural.

This is the same basic idea as English November is but the boys stay.

Pueri is nominative plural.

It comes from puer, meaning boy. In this sentence, pueri is the subject of manent, so it must be in the nominative.

• singular: puer = boy
• plural: pueri = boys

Because domi is the locative form meaning at home.

This is a special idiom. Latin keeps an old locative case in a few words, and domus is one of them.

So:

• domi = at home
• in domo = in the house / inside the home

In many contexts, domi is the more natural way to say at home, while in domo can sound more physically located inside the building.

Because libentius is the comparative adverb.

• libenter = willingly, gladly
• libentius = more willingly, more gladly

Since the sentence is not just saying that the boys stay at home willingly, but that they do so more willingly or rather, the comparative adverb is used.

This is a very common Latin way of expressing an idea that English might translate more loosely as prefer to.

Because it modifies the verb manent, not the noun pueri.

Ask what word it is describing:

• Is it describing the boys? No.
• Is it describing how they stay? Yes.

So Latin uses an adverb:

• libentius manent = they stay more willingly

If it were an adjective, it would describe the boys themselves, which is not the idea here.

Manent is:

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

It comes from maneo, manere, meaning remain or stay.

So manent means they stay or they remain.

Because maneo gives a more specific idea than sum.

• sum = be
• maneo = remain, stay

So pueri domi libentius manent means the boys stay at home, not merely that they are at home.

Latin often prefers a more precise verb where English might sometimes use a simpler one.

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

This sentence has a very natural Latin order, especially with the verb near the end:

• November frigidior est quam October
• et pueri domi libentius manent

But Latin could rearrange parts of the sentence without changing the basic meaning very much, for example:

• et pueri libentius domi manent

The main difference would be emphasis, not core meaning.

Yes. They are real Latin month names and can decline.

For example:

• nominative: November, October
• genitive: Novembris, Octobris
• accusative: Novembrem, Octobrem
• ablative: Novembri, Octobri

In this sentence they are nominative because November is the subject, and October follows quam in the same case.

Because Latin has no articles.

Latin does not have words exactly equivalent to English the or a/an. Whether a noun is understood as a boy, the boy, or just boy depends on context.

So pueri can mean boys or the boys, depending on the situation.