My daughter really enjoyed this one. It took me a bit to properly get into, and time travel always makes my head hurt, no matter how simply it's managed.
This story is told in two points-of-view: Finlay, who's an orphan and attends the Orphanage School, and Honey Bee, whose Uncle owns (and she thus attends) the Brathelthwaite Boarding School (catch the word, "Brat" at the beginning? I think it's deliberate).
The rivalry starts at the Spindthrift Tournament, which reminded me of Field Day in elementary school. Brathelthwaite alleges the Orphanage school broke the rules and wins by default.
Thus starts the war of pranks / rivalry between the schools. At the same time, the Whispering Kingdom, nearby, goes to war against -- well, pretty much everyone. The "whisperers" have a sort of speaking-magic they use to convince people to do things for them. They're kidnapping children, but for what purpose?
And then a boy and a girl start "spying" on the Orphanage School and Brathelthwaite, and they're not Spendthriftians (they look too different) and the kids think they're Whisperers, so they run them down and ... discover they're from the future, and not allowed to talk about it, but they're there to change it.
And there are dragon riders, but you have to wait for the dragons to appear. It's in there, at the very, very end.
This book has many threads, too many to summarize without giving too much away, and then there'd be no point in you reading it, would there? So I won't spoil it. Enjoy the read!