Mater spongiam quaerit, ut pavimentum madidum citius siccare possit.

Because spongiam is the direct object of quaerit (is looking for / seeks).

• spongia = sponge (dictionary form, nominative singular)
• spongiam = sponge as a direct object, so accusative singular

Latin marks the job a noun is doing by its case ending, not mainly by word order. So Mater spongiam quaerit means Mother is looking for a sponge, not A sponge is looking for mother.

Because mater belongs to the third declension, not the first.

A beginner often expects feminine nouns to look like puella, but Latin nouns come in different declensions. Mater, matris is a common third-declension noun meaning mother.

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

This is a very common Latin construction: ut + subjunctive to express purpose.

So:

• ut = so that / in order that
• possit = may be able / can

The clause ut pavimentum madidum citius siccare possit tells us why the mother is looking for a sponge:
so that she can dry the wet floor more quickly.

This is called a purpose clause.

Because after ut in a purpose clause, Latin normally uses the subjunctive, not the indicative.

So:

• potest = she is able / she can (indicative)
• possit = she may be able / can, used here as the present subjunctive

The subjunctive is not making it “less real” in English; it is simply the normal grammar after ut when expressing purpose.

Because it depends on possit.

Latin often uses possum (to be able) with an infinitive, just like English uses can / be able to with a bare verb:

• potest currere = she can run
• possit siccare = she can dry / may be able to dry

So in this sentence:

• possit = can / may be able
• siccare = to dry

Together: can dry

Pavimentum is accusative singular, because it is the direct object of siccare.

The thing being dried is the floor:

• siccare pavimentum = to dry the floor

It happens to look the same as the nominative because pavimentum is a neuter second-declension noun. In many neuter nouns, the nominative and accusative singular have the same form.

Because madidum is an adjective describing pavimentum, and adjectives must agree with the nouns they modify in:

• gender
• number
• case

So:

• pavimentum = neuter singular accusative
• madidum = neuter singular accusative

Together, pavimentum madidum means the wet floor.

Citius is the comparative adverb from cito (quickly), and it means more quickly.

So:

• cito = quickly
• citius = more quickly

In English, we often translate this naturally as more quickly or just faster.

So citius siccare means to dry [it] more quickly / faster.

Yes. Quaerit is present indicative active, third person singular from quaero, quaerere.

Depending on context, quaerere can mean:

• to seek
• to look for
• to search for
• sometimes to try to get / obtain

In this sentence, looks for or seeks fits naturally:
Mother is looking for a sponge...

Latin word order is more flexible because the endings show the grammar.

English depends heavily on order:

• Mother seeks a sponge

Latin can move words around more freely:

• Mater spongiam quaerit
• Spongiam mater quaerit
• Mater quaerit spongiam

These all keep basically the same core meaning, though the emphasis may shift.

In your sentence, the order is quite natural:

• first the main idea: Mother is looking for a sponge
• then the purpose: so that she can dry the wet floor more quickly

The understood subject is the same person as mater: the mother.

Latin often leaves subject pronouns unstated when the verb ending already shows the person and number. Possit is third person singular, so here the sense is:

Mother is looking for a sponge, so that she may be able to dry the wet floor more quickly.

Latin does not need to say ea (she) unless it wants extra emphasis or contrast.

Yes. Ut is a very common word with several uses, so learners often need to figure it out from context.

Some common meanings include:

• as
• when
• so that / in order that
• that after certain verbs of happening or result

In this sentence, because ut is followed by a subjunctive (possit) and explains the purpose of quaerit, it clearly means so that / in order that.