Learn Hardcore German: Wir kümmern uns um die Kinder.

Yes. The core verb is sich (um etwas/jemanden) kümmern, which is reflexive. That means you must use a reflexive pronoun that matches the subject. With wir, the correct reflexive pronoun is uns. You cannot say just “Wir kümmern um …” in standard German; the reflexive is required. Here, the reflexive pronoun is in the accusative case.

What case does the object after "um" take?

After um, you use the accusative. That’s why it’s um die Kinder. A common mnemonic for accusative prepositions is: durch, für, gegen, ohne, um, bis, entlang.

So is "die Kinder" nominative or accusative here?

Accusative plural. Note that nominative plural is also “die,” so the form looks the same; the preposition um tells you it’s accusative.

Where should the reflexive pronoun go in the main clause?

In a main clause, the conjugated verb is in position 2, and the reflexive pronoun usually comes right after it, before other objects/phrases:

Wir kümmern uns um die Kinder.
With an adverb: Wir kümmern uns heute um die Kinder.

How does this look in a subordinate clause?

In a subordinate clause, the conjugated verb goes to the end:

…, dass wir uns um die Kinder kümmern.
…, weil wir uns um die Kinder kümmern.

Can I front "um die Kinder" for emphasis?

Yes. You can put the prepositional phrase first to emphasize it. The finite verb must still be in position 2:

Um die Kinder kümmern wir uns. (emphasis on “the children”)

What is the infinitive and how do you conjugate it in the present?

Infinitive pattern: sich (um + Akk.) kümmern. Present conjugation (with reflexive pronouns):

ich kümmere mich
du kümmerst dich
er/sie/es kümmert sich
wir kümmern uns
ihr kümmert euch
sie/Sie kümmern sich

How do I say it in the perfect (past) tense?

Use “haben” + past participle gekümmert, and keep the reflexive pronoun:

Wir haben uns um die Kinder gekümmert.

What’s the imperative?

du: Kümmere dich um die Kinder!
ihr: Kümmert euch um die Kinder!
Sie: Kümmern Sie sich um die Kinder!

What’s the difference between "sich kümmern um" and "aufpassen auf"?

sich kümmern um + Akk. = take care of/handle responsibilities for someone or something, often ongoing or organizational care. Example: Ich kümmere mich um die Kinder.
aufpassen auf + Akk. = watch/look after/supervise (keep an eye on, babysit). Example: Ich passe auf die Kinder auf.

How does "sorgen für" compare to "sich sorgen um" and "sich kümmern um"?

sorgen für + Akk. = provide for/ensure someone or something is taken care of. Example: Wir sorgen für die Kinder (we provide for them).
sich sorgen um + Akk. = worry about (emotional concern). Example: Wir sorgen uns um die Kinder (we’re worried about them).
sich kümmern um + Akk. = actively take care of/attend to practical needs or tasks. Example: Wir kümmern uns um die Kinder.

Can I say "Wir kümmern die Kinder"?

No. To mean “take care of,” German requires the reflexive construction with um: Wir kümmern uns um die Kinder. Without the reflexive and preposition, kümmern means “to concern/affect” someone: Das kümmert mich nicht (“That doesn’t concern/bother me”).

How do I replace "die Kinder" with a pronoun?

People/things already mentioned: Wir kümmern uns um sie.
Referring back to an idea or a thing with “um”: Wir kümmern uns darum. Note: um sie (them) vs. um Sie (formal “you”) is distinguished by capitalization in writing.

How do I form a question with this verb?

Yes/no question: Kümmert ihr euch um die Kinder?
With a question word (prepositional adverb): Worum kümmert ihr euch? (What are you taking care of?)
Asking about a person: Um wen kümmert ihr euch?

Are contractions like "ums" possible here?

Only with neuter singular: ums = um das. Since Kinder is plural (die), you cannot contract it: you must say um die Kinder, not “ums Kinder.”

What are the reflexive pronoun forms I need?

Accusative: mich, dich, sich, uns, euch, sich Dative (for other verbs that use dative reflexives): mir, dir, sich, uns, euch, sich For sich kümmern, use the accusative set.

Does "sich kümmern" ever take the dative reflexive?

No. sich kümmern uses the accusative reflexive. Some other verbs use dative reflexives (e.g., Ich merke mir…, Ich wasche mir die Hände), but not sich kümmern.

Is "um" here a separable prefix?

No. um is a preposition governing the accusative, not a verb prefix. The verb is kümmern; the pattern is sich kümmern um ….

Any pronunciation tips for "kümmern"?

ü is a front rounded vowel; round your lips while saying an “ee” sound: kü.
Stress the first syllable: KÜM-mern.
The double “m” keeps the vowel short.

Can I use "sich kümmern um" with things, not just people?

Yes. It’s very common for tasks and arrangements: Ich kümmere mich um die Tickets. / Kannst du dich um den Termin kümmern?

Are there common colloquial variants?

darum often becomes drum in speech: Kümmer dich drum! (colloquial for Kümmere dich darum!)
In fast speech, you’ll also hear the short imperative Kümmer dich …, though the full Kümmere dich … is the standard form.