grass or grain?

Maybe grain is a grass....? But anyway, northeast arizona has a buch of different grasses. This is one that i have not seen before. The local rancher left and took his cattle with him so plants that normally get chomped are getting a chance to grow.

I found these growing in an area where a tribe (pottery chards say Anasazi) had built a water catchment tanks.
Maybe something left over from them?

looks similar to something that grew out of some straw mulch we used.

the one we had looked like grass until it got ~5ft tall, then it sorta looked like a grain.

Looks very much like northern or thick spike wheatgrass (Elymus lanceolatus), a common native grass on the Great Plains.