If you’ve been learning Portuguese for a few months, then you probably already know that homework = dever de casa. Simple, right? Well, it would be if Brazilians said dever de casa as much as we say homework, but in reality there are a mixture of words to describe the particular type of assignment.
First, let’s look at some other ways of saying homework. One could say tarefa de casa, but this is easily confused with housework/household chores (tarefa caseira, trabalho doméstico). Better to stick with lição de casa (most clear), dever/tarefa de escola, tarefas escolares, or perhaps trabalhos pra/de casa as alternatives.
…Back to ways of saying different types of assignments. As I mentioned, dever de casa just isn’t used as commonly as we use homework in the US, so in approximate order of importance, here are some ways of describing types of assignments::
redação* (writing (about a chosen subject), composition)
ensaio (essay, test)
tarefa (job/task, in general)
reportagem (article, report)
resumo (summary, abstract)
(also, fazer uma prova means take a test. While speaking some people will say simply fazer prova which in other contexts can mean to prove, demonstrate, or have courage)
(*) Some of you may disagree with putting redação at the top of the list. This comes from experience in Minas Gerais where this type of assignment was most common, and in my head I learned to associate it with homework.
“Do your homework” in the sense of “Perform your duties”
Finally, in the US we often ask “Have you done your homework?” in the sense of “Have you done sufficient research?”, i.e., “Do you know what the hell you’re talking about?“. There are various ways of saying this, perhaps try:
cumprir deveres; cumprir a missão
fazer bem (o trabalho (de casa)); fazer o que (lhe) compete; fazer o que tem de fazer/realizar; fazer uma série de trabalhos de casa; fazer uma boa preparação
preparar matéria suficientemente