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.
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.
problem
'das Problem' and 'die Hausaufgabe' can both mean something that you have to work on or solve. 'das Problem' is more general and fits when something is difficult or needs a solution. 'die Hausaufgabe' usually means an assignment from school or university that you do at home. Figuratively, 'Hausaufgabe' can also mean a task for adults, companies, or politics. Learners may confuse the words because both have to do with tasks. As a practical rule: at school, people often say 'Hausaufgabe'; for a difficulty in everyday life, 'Problem' is more likely.
Mein Vater sagt, dass die Familie im Sommer ihre Hausaufgaben für den Umzug machen muss.
My father says that the family has to do its homework for the move in the summer.
Im Gespräch mit einem Freund hat sie ihr Problem bei der Arbeit erklärt.
In a conversation with a friend, she explained her problem at work.