Although Thomas Caldecot Chubb's book, The Byzantines, is out of print, it would be a good book for any homeschooling family to buy or borrow.
Mr. Chubb asks, "Why should you and I care about Constantinople and the Byzantine Empire?" Then, in only 116 pages, he proceeds to answer that question. The answer in a nutshell is this: "For more than a thousand years, it... carried the torch of Western civilization, a torch that had been given to it by the Greeks and Romans."
Of course, along the way we learn the history of Byzantium, about the people, about life there, and how and why the empire ended.
Included are a chronological chart of the Byzantine Empire and world events and a list of recommended books for additional reading. Reading level is probably 6th to 8th grades.