Thank you. I did realize that it was plural genitive but I'm trying to figure out how I would figure that out. I don't know the root of дети, so I'm having a hard time.
Yandex says that child (not ребенок), singular is дитя - but says it's neuter, I think. And I don't know how to handle a neuter ending with я. And that may not even be right.
If there's a pattern to why it changes to that in genitive that I can apply to other words then I'd like to know it - but I just can't find it. It may just be irregular and something I need to memorize, which is fine. With most of the cases I can generally figure out the right answer or figure out where I went wrong. With this one, I'm lost.
Thank you again.
Genitive case follows the preposition "у", so you could use this information to help you determine which case to put the word in. The word "дитя" isn't used that often, usually it's just "ребёнок" for singular and "дети" for plural. And you're right in thinking that "дети" is irregular, so you'll just have to memorize the different case endings for it.
I was just looking this all up in Wiktionary, so here are some links for figuring this out (which contain more links, if you're interested):
On top of what's been said already, words will have a genitive plural form in -ей if the ending is soft (soft vowel or ь), velar/soft palate (g, k, or the Scottish ch in loch which is х in Russian), or what's sometimes called a "hush", which means a ch, sh, or the g in beige sound. As Janisa said, the uncommon nominative singular form here is дитя, which ends in a soft adjective. So in this sense the genitive plural ending is actually regular.