Learn Hardcore Croatian: U dvorani moramo paziti na djecu. - In the hall we have to watch the children.

In u dvorani, the noun is in the locative singular: dvorani.
Many Croatian prepositions use the locative case to express location, and u (in) is one of them when it means “inside something (no movement)”.

So:

dvorana – nominative (dictionary form, subject)
- Dvorana je velika. – The hall is big.
u dvorani – locative (after u = in, at, when talking about location)
- U dvorani je hladno. – It is cold in the hall.

So u dvorani literally means “in the hall” as a location, and that is why dvorani is used, not dvorana.

What is the difference between u dvorani and u dvoranu?

The difference is static location vs motion into:

u dvorani – locative case, used for being somewhere:
- U dvorani moramo paziti na djecu.
  We must be careful with the children in the hall. (we are already there)
u dvoranu – accusative case, used for movement into a place:
- Idemo u dvoranu.
  We are going into the hall.

So:

Gdje smo? – U dvorani. (Where are we? In the hall.)
Kamo idemo? – U dvoranu. (Where are we going? Into the hall.)

What exactly does moramo mean, and what is the full verb?

Moramo is the 1st person plural present tense of the verb morati.

morati = must, have to, be obliged to
moramo = we must / we have to

So:

Moramo paziti na djecu. – We must / have to watch the children.

In Croatian you normally drop the pronoun mi (we), because moramo itself already shows that the subject is we:

Mi moramo and just Moramo both mean We must, but Mi is usually omitted unless you want to emphasize we.

What is the difference between morati and trebati in this kind of sentence?

Both express necessity, but they are used a bit differently:

morati – must, have to
Stronger, more obligatory, like a rule or duty.
- Moramo paziti na djecu. – We must / have to watch the children.
trebati – need to, should
Often a bit softer or more neutral, more like a need or recommendation.
- Trebamo paziti na djecu. – We need to / should watch the children.

In everyday speech, people sometimes use them almost interchangeably, but morati feels stronger and more obligatory than trebati.

What does paziti na mean here? Is it be careful or look after?

The verb paziti has several related meanings, and paziti na nekoga / nešto can mean:

to be careful about something / to pay attention to something
to look after / watch over someone, especially children

In this sentence, with na djecu, the natural English equivalents are:

to look after the children
to watch the children
to keep an eye on the children

The nuance is actively paying attention so that nothing bad happens to the children.

Why is it paziti na djecu and not just paziti djecu?

The most common structure in standard speech is paziti na + accusative:

paziti na djecu – pay attention to / look after the children

You can sometimes hear paziti djecu, and it can also be understood as looking after the children, but:

paziti na djecu is more neutral and standard,
paziti djecu can feel a bit more like taking care of them as a task (similar to čuvati djecu).

For learners, it is safest to use paziti na + accusative when you mean to watch / be careful about / pay attention to something or someone.

Why is it na djecu and not na djece? What case is djecu?

Djeca (children) is a special, irregular noun, but in this sentence:

djecu is accusative plural.

The preposition na can take accusative (often with direction or target of attention) or locative (location), depending on meaning. With paziti na, it takes accusative:

paziti na djecu – watch the children (accusative)
paziti na cestu – watch the road (accusative)
paziti na vrijeme – watch the time (accusative)

Djece is the genitive form and would not be used with paziti na in this sense. So na djecu (accusative) is the correct form here.

How is djeca / djecu related to dijete? Why is the plural so different?

This is an irregular pattern:

dijete – child (singular)
djeca – children (plural, nominative)
djecu – children (accusative; the form in the sentence)

A few important forms:

nominative: dijete (one child), djeca (children)
accusative: dijete, djecu
genitive: djeteta, djece
dative/locative: djetetu, djeci
instrumental: djetetom, djecom

So in paziti na djecu, you’re seeing accusative plural of djeca.

Why is there no word for we in the sentence? Where is mi?

The subject pronoun mi (we) is simply omitted, because Croatian is a pro‑drop language: the verb ending shows who the subject is.

Moramo – 1st person plural (we)
Mi moramo – We must
Moramo – We must (same meaning; mi is understood)

So:

U dvorani moramo paziti na djecu. – perfectly normal, default
U dvorani mi moramo paziti na djecu. – still correct, but mi is added for emphasis (we as opposed to someone else).

Can the word order change? For example, is Moramo paziti na djecu u dvorani also correct?

Yes, Croatian word order is more flexible than English. All of these are grammatically correct, with slightly different emphasis:

U dvorani moramo paziti na djecu.
Neutral; sets place first: In the hall, we must watch the children.
Moramo paziti na djecu u dvorani.
Starts with what we must do; the phrase u dvorani feels like an additional detail at the end.
Na djecu moramo paziti u dvorani.
Emphasizes the children; could sound contrastive (e.g., the children, not something else).

The most natural options in many contexts would be the first two. Meaning stays essentially the same.

Could I use a different verb instead of paziti to say look after the children?

Yes, there are a few common alternatives, with slightly different nuances:

čuvati djecu – to look after / babysit / guard the children
More about protecting and taking care of them.
brinuti se za djecu – to worry about / take care of the children
Focuses on caring, concern, responsibility.
gledati djecu – literally to look at the children;
can mean visually watching them, but not necessarily taking care of them.

In your sentence, paziti na djecu nicely combines the ideas of paying attention and taking care / keeping them safe.

Is u dvorani the only way to say in the hall, or can I say u sali?

You can sometimes hear both:

dvorana – hall (often larger: sports hall, concert hall, etc.)
sala – also hall / room, often used for:
- sala za sastanke – meeting room
- sala za vjenčanja – wedding hall
- operacijska sala – operating room

In many contexts:

u dvorani – in the hall (especially sports halls, gymnasiums, big halls)
u sali – in the hall/room (can be more general or specific to certain types of rooms)

In a school or sports context, u dvorani (sports hall, gym) is very common.