Awhile versus A While

As I get older I seem to become more forgetful, and have problems with stuff I once knew well. However, with “awhile” versus “a while” I think I have generally always had problems remembering the correct usage. Here is how it should be:

“Awhile” is an adverb. It means “for a while.” As an adverb, “awhile” usually modifies a verb – as in “I will wait awhile.”

“While” is a noun. It means “a period of time” (and “a” is an indefinite article modifying it). Usually, the two words “a while” is used when following a preposition – as in, “I will wait for a while” – or with the words ago or back (a while ago; a while back).