Solution 1:

Crap was originally used to mean (according to the Oxford English Dictionary):

  1. The husk of grain; chaff. Obs.

This meaning is circa 1440. It was also used to mean:

The residue formed in rendering, boiling, or melting fat; cracklings, graves; hence crap-cake, tallow-craps. In this sense it varies with scraps. (Usually in pl.)

This meaning is dated around 1490. In any case, the term was used to mean "rejected or left matter, residue, dregs, dust." However, the OED is not sure whether all the senses of the word were tied to the same roots, even though they share a common notion. They write,

Identical with earlier Dutch krappe ‘carptus, carptura, res decerpta, frustum decerptum siue abscissum, pars abrasa siue abscissa; pars carnis abscissa; crustum; offella, offula; placenta; pulpamentum’ (Kilian, 1599), connected with krappen to pluck off, cut off, separate. Compare also French crape, Old French crappe siftings, also ‘the grain trodden under feet in the barn, and mingled with the straw and dust’ (M. L. Delisle in Godefroy), medieval Latin crappa in Du Cange. (Compare also crapinum the smaller chaff.)

In modern French the word has taken the sense of ‘dirt, filth’, and ‘grease of a millstone’. It is doubtful whether all the senses here placed belong to one word, though a common notion of ‘rejected or left matter, residue, dregs, dust’ runs through them.

The slang usage of the term dates from 1970.