1
general::
Do or take part in half-heartedly, as in She was just playing at keeping house, letting the others do all the work. [Mid-1800s]
American Heritage Idioms
2
general::
Phrase(s): play at something
to pretend to be doing something. • You are not fixing the car, you are just playing at repair work! • Stop playing at doing the dishes and get the job done.
McGrawhill's American Idioms And Phrasal Verbs