Learn Hardcore German: Alle Fehler in den Hausaufgaben sollen im Unterricht korrigiert werden. - All mistakes in the homework should be corrected in class.

Even though in English you might think the teacher corrects the mistakes, in German this sentence is in the passive voice:
Alle Fehler … sollen … korrigiert werden.
Literally: All mistakes … shall be corrected.

In a passive sentence, the thing that undergoes the action (here: the mistakes) becomes the grammatical subject, so it appears in the nominative: Alle Fehler.

What case is Alle Fehler, and why?

Alle Fehler is in the nominative plural.

Fehler (mistake) – masculine noun
- Singular nominative: der Fehler
- Plural nominative: die Fehler, but when you add alle, you get alle Fehler (no article needed).

It is nominative because it is the subject of the sentence.

Why is it in den Hausaufgaben and not in die Hausaufgaben?

The preposition in can take either dative (location) or accusative (direction).

Here it expresses location (where the mistakes are), so it takes the dative:

Plural definite article:
- Nominative: die Hausaufgaben
- Dative: den Hausaufgaben

Because this is plural dative, you get in den Hausaufgaben, meaning in the homework (assignments), referring to where the mistakes are found.

Why is den Hausaufgaben dative plural with -en, and not something like Hausaufgabens?

The basic forms are:

Singular: die Hausaufgabe
Plural: die Hausaufgaben

In the dative plural, German usually adds -n to the noun if it doesn’t already end in -n or -s.
Hausaufgaben already ends in -en, so no extra change is needed.

So:

Nominative plural: die Hausaufgaben
Dative plural: den Hausaufgaben (article changes; noun stays the same)

What does Hausaufgaben mean exactly, and is it usually plural?

Hausaufgabe literally means home task / homework assignment.

In practice:

Singular: die Hausaufgabe – one specific assignment
Plural: die Hausaufgaben – homework in general or several tasks

Very often, German speakers use the plural Hausaufgaben where English would simply say homework (uncountable). So in den Hausaufgaben here really just means in the homework.

What case is im Unterricht, and what does im stand for?

Im Unterricht is dative singular.

im is a contraction of in dem
Unterricht (instruction / class / lessons) is masculine:
- Dative singular: dem Unterricht

So:

in dem Unterricht → contracted to im Unterricht

It means in class / during the lesson(s).

Why is there no article like der Unterricht here; why just Unterricht?

In this context, Unterricht is used in a general / abstract sense, similar to English in class or during lessons, not a specific class like the math lesson.

German often omits the article with certain abstract or mass nouns used in a general way (e.g. Schule, Unterricht, Krieg, Frieden).

So im Unterricht is understood as in class in general, not in the specific lesson.

What is the role of sollen in this sentence? Why not just werden korrigiert?

Sollen is a modal verb expressing obligation, expectation, or plan — similar to should or are supposed to.

Alle Fehler … werden korrigiert.
= All mistakes are corrected. (neutral statement of fact)
Alle Fehler … sollen … korrigiert werden.
= All mistakes are supposed to be corrected. / All mistakes should be corrected.

So sollen adds the idea that this is a requirement, rule, or plan, not just a description of what (in fact) happens.

Why do we need both sollen and werden? Why not Alle Fehler sollen im Unterricht korrigiert or … sollen korrigiert werden werden?

In German passive with a modal verb is formed with:

finite modal verb in position 2 (sollen)
Participle II of the main verb (korrigiert)
Infinitive of werden at the end (werden)

Pattern:
Alle Fehler … sollen … korrigiert werden.

You cannot drop werden, because korrigiert alone would just be a participle without a passive auxiliary.

You also cannot say werden werden; German does not stack two forms of werden like that in this structure. The passive is marked only once, by werden in the infinitive at the end: korrigiert werden.

What exactly is the tense and voice of sollen … korrigiert werden?

Tense: Present (Präsens)
Voice: Passive (Vorgangspassiv)
With a modal verb (sollen)

So the structure is:
Modal (present) + main verb participle + werden (infinitive)
= present passive with a modal, equivalent to English should be corrected / are to be corrected.

Why is sollen in the second position and korrigiert werden at the end?

Standard main-clause word order in German:

Position 1: one element (here: Alle Fehler in den Hausaufgaben)
Position 2: finite verb (here: sollen)
Middle field: the rest (here: im Unterricht)
End field: other verb forms (infinitives, participles)

So:

Alle Fehler in den Hausaufgaben – position 1 (subject phrase)
sollen – finite verb in position 2
im Unterricht – middle
korrigiert werden – non-finite verb cluster at the end

This is the typical German structure for a main clause with a modal plus passive.

Could the word order be different, for example starting with Im Unterricht?

Yes. You can move elements around as long as the finite verb stays in second position. For example:

Im Unterricht sollen alle Fehler in den Hausaufgaben korrigiert werden.
In den Hausaufgaben sollen im Unterricht alle Fehler korrigiert werden.

The meaning stays essentially the same; you just change the emphasis:

Starting with Im Unterricht highlights in class.
Starting with Alle Fehler highlights all mistakes as the topic.

Why is it alle Fehler and not alle die Fehler?

With plural nouns, alle usually replaces the article:

die Fehler = the mistakes
alle Fehler = all (the) mistakes

So you normally say:

alle Menschen, not alle die Menschen
alle Bücher, not alle die Bücher

Alle die Fehler is only usable in a special, emphatic context (roughly: all those mistakes), and even then many speakers would prefer all diese Fehler. In this neutral sentence, alle Fehler is the correct and natural choice.

Why is Fehler the same form in singular and plural?

Fehler is one of those masculine nouns whose plural looks like the singular:

Singular: der Fehler (one mistake)
Plural: die Fehler (several mistakes)

You tell singular/plural apart by:

The article: der vs die
Or by words like ein vs viele / alle etc.

So in alle Fehler, you know it’s plural from alle.

Could I say Alle Fehler sollen im Unterricht in den Hausaufgaben korrigiert werden? Does the position of in den Hausaufgaben matter?

You can move in den Hausaufgaben, but some positions sound more natural than others.

Very natural:
- Alle Fehler in den Hausaufgaben sollen im Unterricht korrigiert werden.
  (restricts Fehler: only those in the homework.)

If you say:

Alle Fehler sollen im Unterricht in den Hausaufgaben korrigiert werden.

it is grammatically possible, but it sounds less clear, as if in den Hausaufgaben modified korrigiert werden (as if the correction somehow happens in the homework), rather than specifying which mistakes. Native speakers usually put in den Hausaufgaben right after Fehler to clarify which mistakes.

Why is the preposition in used with den Hausaufgaben and dem Unterricht, not something like bei or an?

In indicates inside / within something (either physically or abstractly):

in den Hausaufgaben – the mistakes are in the homework exercises
im Unterricht – something happens during / in class

Alternatives would change the nuance:

bei den Hausaufgaben – more like while doing the homework or with the homework
an den Hausaufgaben – usually working on the homework (arbeiten an den Hausaufgaben)

So in is the most natural choice for mistakes located within the homework and corrections during the class.

Could I use müssen instead of sollen? What would be the difference?

Yes, you can say:

Alle Fehler in den Hausaufgaben müssen im Unterricht korrigiert werden.

Difference in nuance:

sollen – are supposed to, should, often a rule, plan, or external expectation (e.g. from the teacher, school, curriculum).
müssen – must, stronger obligation, necessity, no real choice.

In many contexts they can overlap, but müssen sounds more strict / unavoidable, while sollen sounds more like a guideline or requirement.

Why is the passive used instead of an active sentence like Der Lehrer soll alle Fehler … korrigieren?

The passive allows you to focus on the action and its object (the mistakes), rather than on the agent (who corrects them).

Active: Der Lehrer soll alle Fehler in den Hausaufgaben im Unterricht korrigieren.
– Focus on the teacher doing it.
Passive: Alle Fehler in den Hausaufgaben sollen im Unterricht korrigiert werden.
– Focus on the mistakes and the requirement that they be corrected.

In instructions, rules, and official statements, German often uses the passive to sound more impersonal and general.

Is this sentence formal, or is it something you would actually hear in a normal classroom?

The sentence is completely natural and would fit both spoken and written contexts.

A teacher might say something very close to this in class:
Alle Fehler in den Hausaufgaben werden / sollen im Unterricht korrigiert.
In a written rule (e.g. school policy), the exact wording
Alle Fehler in den Hausaufgaben sollen im Unterricht korrigiert werden.
sounds appropriate and neutral-formal.

So it’s standard, neutral German.