Learn Hardcore German: Die Dozentin erklärt uns die Reihenfolge, in der wir die Übungen bearbeiten sollen. - The lecturer explains to us the order in which we are supposed to work on the exercises.

Dozent (m.) / Dozentin (f.): academic teacher, lecturer, instructor (often not for small children, but for adults, university students, etc.).
Lehrer (m.) / Lehrerin (f.): schoolteacher, usually for primary or secondary school.

So Die Dozentin suggests this is likely at a university or in some kind of course for adults, not a regular school.

Why is it uns and not wir in Die Dozentin erklärt uns die Reihenfolge?

Wir is the nominative form (subject: we).
Uns is the dative (to us/for us) and also the accusative (us) form.

In the sentence:

Die Dozentin = subject (nominative): The lecturer
erklärt = verb: explains
uns = indirect object (dative): to us
die Reihenfolge = direct object (accusative): the order / sequence

German uses erklären + Dativ-Person + Akkusativ-Sache:

jemandem etwas erklären = to explain something to someone

So it must be uns (to us, dative), not wir.

Which case is die Reihenfolge in, and how can I see that from the form?

In Die Dozentin erklärt uns die Reihenfolge, die Reihenfolge is in the accusative singular.

You can tell because:

The basic pattern is jemandem etwas erklären:
- jemandem (dative) = uns
- etwas (accusative) = die Reihenfolge

For feminine nouns, die looks the same in nominative and accusative singular:

Nominative: die Reihenfolge (subject)
Accusative: die Reihenfolge (object)

So the form die alone doesn’t tell you the case; you have to look at the verb pattern and sentence roles. Here, die Dozentin is the subject, so die Reihenfolge must be the object (accusative).

Why is it erklärt uns die Reihenfolge and not something like erklärt die Reihenfolge zu uns?

German doesn’t use zu here. The verb erklären already includes the idea to someone when you use a dative:

jemandem etwas erklären = to explain something to someone

So:

Die Dozentin erklärt uns die Reihenfolge. ✅
The lecturer explains the order to us.

If you tried:

Die Dozentin erklärt die Reihenfolge zu uns. ❌

this would sound wrong to a native speaker. The preposition zu is simply not used with erklären in this sense; the role of to us is expressed by the dative pronoun uns.

What is the role of the comma before in der wir die Übungen bearbeiten sollen?

The comma separates the main clause from a relative clause:

Main clause: Die Dozentin erklärt uns die Reihenfolge
Relative clause: in der wir die Übungen bearbeiten sollen

In German, subordinate clauses (including relative clauses) must be separated by a comma from the main clause. So the comma is mandatory, not optional, in standard written German.

What does the in der at the start of the relative clause mean, and why der?

In der is made up of:

in = preposition (in, in which)
der = relative pronoun (here: feminine, dative, singular)

The relative pronoun der refers back to die Reihenfolge:

Reihenfolge is feminine singular.
After in, we need the dative case here (because it’s not movement into something, but the static order in which we do something).

So we get:

in + der (feminine dative singular) → in der

Literally: the order, *in which we are supposed to work on the exercises.*

Why is the word order in the relative clause in der wir die Übungen bearbeiten sollen, with sollen at the end?

German has a strong word-order rule:

In main clauses, the conjugated verb is in second position.
In subordinate clauses (like relative clauses), the conjugated verb goes to the end.

Here, sollen is the conjugated verb (1st person plural wir sollen), and the whole thing is a subordinate clause introduced by in der. So the verb must go to the end:

in der wir die Übungen bearbeiten sollen ✅

If this were a main clause, you could say:

Wir sollen die Übungen in dieser Reihenfolge bearbeiten.

Here, sollen is in second position, as expected for a main clause.

Why is it bearbeiten sollen and not sollen bearbeiten at the end?

In a subordinate clause with a modal verb (like sollen) plus another verb (like bearbeiten), German puts the full verb before the modal verb at the end:

… dass wir die Übungen bearbeiten sollen.
… weil wir die Übungen machen müssen.

Pattern: [subordinate conjunction] … [other elements] [full infinitive] [modal verb (infinitive or finite, depending on structure)]

So in this relative clause:

subordinate clause → verb(s) go to the end
modal construction → bearbeiten before sollen

Hence: … die Übungen bearbeiten sollen is the normal order.

What’s the nuance of bearbeiten here compared to just machen?

Both can often be translated as to do, but:

machen is very general: to do, to make.
bearbeiten is more specific: to work on, to process, to work through something, often systematically and thoroughly.

For exercises, homework, tasks, etc., bearbeiten often sounds more formal and precise than machen.

So:

die Übungen machen = do the exercises (neutral, common in speech)
die Übungen bearbeiten = work through the exercises (slightly more formal/academic-sounding, appropriate for a lecturer speaking to students)

What does sollen express in this sentence? Is it like must or should?

Sollen often sits between must and should, depending on context. Here it expresses a requirement / instruction from an authority (the lecturer):

… in der wir die Übungen bearbeiten sollen.
→ … in which we are supposed to work on the exercises.
→ … in which we should work on the exercises (as instructed).

It’s not quite as forceful as müssen (must, have to), but it clearly indicates that this is the intended or required order, not just a suggestion you can freely ignore.

Why is it die Übungen and not den Übungen?

Die Übungen here is the direct object of bearbeiten, so it’s in the accusative plural.

Nominative plural: die Übungen
Accusative plural: die Übungen

For plural nouns, die is the same in nominative and accusative.

Den Übungen would be dative plural, e.g.:

mit den Übungen = with the exercises
bei den Übungen = during the exercises

In wir die Übungen bearbeiten, the exercises are what we are working on (direct object), so accusative → die Übungen.

Could I say Die Dozentin erklärt uns, in welcher Reihenfolge wir die Übungen bearbeiten sollen instead? Is that equivalent?

Yes, that’s a very natural alternative and means essentially the same thing.

Original:
- Die Dozentin erklärt uns die Reihenfolge, in der wir die Übungen bearbeiten sollen.
  Focus: the order as a thing (she explains the order to us), then defining which order with a relative clause.
Alternative:
- Die Dozentin erklärt uns, in welcher Reihenfolge wir die Übungen bearbeiten sollen.
  Here, in welcher Reihenfolge is a content clause (what she explains), roughly:
  The lecturer explains to us in which order we are supposed to work on the exercises.

Both are correct; the second one slightly shifts the structure but the practical meaning is the same.