I’m sorry, but I believe the accepted answer is wrong.
The “half (of) a NUMBER” construct works like “a lot of SOMETHING” or “a few of SOMETHING” does, in that the verb should agree with the number of the noun that follows those constructs, not with something like half or lot or few, even though each of those is by itself nominally singular.
This is what is called a predeterminer, and it does not affect the grammatical concordance of the noun it modifies with that noun’s verb. In works like an adjectival phrase, if you would. From Cognitive English Grammar, by Günter Radden and René Dirven:
More rarely, a quantifier occurs before a determiner; in this function quantifiers are usually described as predeterminers. . . . More rarely, a quantifier may precede an indefinite determiner as in half a dozen or half a million, where the quantifier half describes a clear subset of a well-defined set.
You can find no end of examples in examples of such things retaining their plural number in printed literature, and none of them becoming singular. Here are just a few:
- Yet not a hundred people in that battle knew for what they fought, or why; not a hundred of the inconsiderate rejoicers in the victory, why they rejoiced. Not half a hundred people were the better for the gain or loss. Not half–a–dozen men agree to this hour on the cause of merits. . . . [Dickens]
- Here were half a hundred boys not looking for favors or tips at this season of the year when the average individual is inclined to be generous, but half a hundred boys who were out the help others. . . . [Boys’ Life]
- A million cascade brooks unite to form a thousand torrent creeks ; a thousand torrent creeks unite to form half a hundred rivers beset with cataracts ; half a hundred roaring rivers unite to form the Colorado, which rolls, a mad, turbid stream, into the Gulf of Colorado [Powell]
- The half a hundred houses of the big village were dark. [O Henry]
- A further half-a-million Germans were deported in WWII from their age- old home in the Volga region. . . . [Central Asia]
- YES, over half a million delighted men and women all over the world have learned music this quick, easy way. [Popular Mechanics]
- Because half a dozen grasshoppers under a fern make the field ring with their importunate chink, whilst thousands of great cattle, reposed beneath the shadow of the British oak, chew the cud and are silent, [Quote It Completely!: World Reference Guide to More Than 5,500 Memorable ...]
- Half a dozen women were setting tables for the evening supper; half a dozen more were busy in the kitchen. . . . [Boys’ Life]