私はローマに住んでいた時に子供でした。
I didn't understand "住んでいた時". I would like a explanation about this structure and a translation.
私はローマに住んでいた時に子供でした。
When I was in Rome, I was a child.
とき(に) means "when ～". See this article.
As you can see in the link, とき here is just a noun that means "time". So once you have learned how to modify a noun (e.g., using an adjective or a relative clause), you can use various ways to say "when ～".
As pointed out in the comment section, this sentence is a bit unnatural because the main subject (私は) and the main predicate (子供でした) are far apart.
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This is exactly what I needed, thank you for your answer, the link and your remarks, they are really useful!– Dav7nSep 27 '16 at 18:52
As others have pointed out, the sentence sounds weird. To answer your question:
住む is the verb "to live".
= > 住んで is the "te" form of the verb — a verb form used in many ways.
= > 住んでいる is the "te-iru" form of the verb. This means "living".
= > 住んでいた is the past tense of the "te-iru" form of the verb. This means "was living".
時 is simply "time".
Therefore 住んでいた時 means "the time when I was living".
私はローマに住んでいた時に子供でした。<- This sentence sounds a bit unnatural... (I'd rather say something like ローマに住んでいたとき、私はまだ子供でした or 私は、ローマに住んでいたとき(に)はまだ子供でした) Did you find it in your book/textbook?