
die Hausaufgabe
homework
An assignment that school pupils or university students get from school or university to complete at home.
Ich muss heute Abend noch meine Hausaufgaben für Mathematik machen.
I still have to do my math homework this evening.
homework
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homework
An assignment that school pupils or university students get from school or university to complete at home.
Ich muss heute Abend noch meine Hausaufgaben für Mathematik machen.
I still have to do my math homework this evening.

task
(Figurative) A problem or task that a person, group, or institution has to solve or work on.
Die neue Regierung hat die Hausaufgabe, die steigenden Energiepreise in den Griff zu bekommen.
The new government has the task of getting rising energy prices under control.
The word is made up of 'Haus' (house/home) and 'Aufgabe' (task/assignment). So it literally describes a task that you are supposed to complete at home.
Die Kinder müssen nach der Schule ihre Hausaufgaben machen.
The children have to do their homework after school.
In a school context, 'Hausaufgabe' (homework) is combined with certain verbs: pupils 'machen' (do) or 'bekommen' (get) homework, while teachers 'aufgeben' (assign) or 'kontrollieren' (check) it.
Der Lehrer hat uns für heute keine Hausaufgaben aufgegeben.
The teacher didn't assign us any homework for today.
You can recognize the figurative meaning from the context. If politics, business, or companies are being discussed rather than pupils, it usually means a task that needs to be solved.
Die wichtigste Hausaufgabe für das Unternehmen ist die Senkung der Kosten.
The most important task for the company is reducing costs.
The expression 'seine Hausaufgaben machen' (to do one's homework) is often used figuratively. It then means that someone, such as a politician or a company, has to prepare well for a situation.
Die Opposition findet, die Regierung habe bei diesem Thema ihre Hausaufgaben nicht gemacht.
The opposition thinks the government has not done its homework on this issue.
housework / term paper
Both words refer to an assignment that learners complete at home for school or university. A Hausaufgabe is usually a single or ongoing exercise, whereas a Hausarbeit is a longer written paper submitted as assessed work. Use „Hausaufgabe“ for smaller assignments and „Hausarbeit“ for more substantial papers.

Für morgen muss ich noch die Hausaufgabe zur Vorlesung bearbeiten.
For tomorrow, I still have to work on the homework for the lecture.
Bis zum Ende des Semesters muss ich eine Hausarbeit über dieses Thema schreiben.
I have to write a term paper on this topic by the end of the semester.