"They" is a singular pronoun
Going by your example, the word children is singular. In reality, it is not singular, just like "they" is not singular. In your sentence, you referred to the word they, which is singular, as there is only one word that is spelled t-h-e-y. If you are using they as a pronoun, like the Constitution is, then it is plural. Here is an example snippet from a sentence in the Constitution: "If they approve of it they should sign it." Since this is talking about one person, the President, the sentence should read: "If he or she approves of it he or she should sign it."
"he or she" is unfair to non-gender-conforming individuals though
