So describing the siege of Kiev as the “end” of Kievan Rus’ is kind of a cop out, akin to identifying Odoacer’s conquest of Rome in 476 as the “end” of the Western Roman Empire. It’s not not true, and it is a sort of dramatic punctuation mark on which to hang a basic understanding of events. It’s a clean break point that a high school student can remember, at least long enough to get through the test. But just as Rome hadn’t been “Rome” for quite some time before 476, so Kiev had stopped being “Kiev” well before the Mongols showed up. Of course, it really stopped being Kiev after they left.