I'd say a better translation of Es sind zehn Kinder is "They are ten children".

A meaning of "there are" would be more plausible if a location is mentioned, e.g. Es sind zehn Kinder auf dem Eis. = There are ten children on the ice.

I'm not sure how to explain the difference in meaning between that and Es gibt zehn Kinder auf dem Eis. -- I'd translate them the same way in English so I lack words to express how they feel different inside me. The difference is fairly subtle so you might not have to worry about it.

Without a location, though, using es sind for "there are" feels poor to me.

This is one of the sentences from the Pearson cooperation, so I think they should be doing the explaining here.