Even Duolingo itself thinks so! I put "fam" as a joke and it said the correct word should be "household".
I agree with Ethan, Kazoku is more frequently used for family than Katei in my experience.
I sent feedback to the Duolingo team that they should include furigana (kanji + hiragana on top) for situations like this.
This course is still in beta, so hopefully we can see that in the full version.
Like Led Zeppelin says:
Cuz you know sometimes words have 2 meanings....
Except with Japanese it can be much more!!!
Duolingo dont really indicate timelines or even plans. I wouldn't expect it to happen in the short term at all sadly.
Kazoku is family why is it katei if its asking for family not household or home.
Seems like "katei" is more like the family unit?
Like if someone was saying "you need to get a job and help support the family", or if you were talking about the concept of the family?
Referring to the group as a unit instead of individuals.
In what frequent context does 'household' get used? Is this a useful beginner word to learn?
Some other common translations of the word are "family" and "home". Some phrases in which it's used are listed here: https://eow.alc.co.jp/search?q=%E5%AE%B6%E5%BA%AD
Essentially, it's used in cases where you're talking about matters related to the family/home but not necessarily the house itself. It's a pretty low-level (N5) kanji word.
So is there some kind of context thing going on here where you might use kazoku when talking about stuff with your friends but when your teacher asks you to list your family members they'd use katei?