see something with half an eye—see or understand smth. very clearly or easily:
- The teacher could see with half an eye that Jim was going to have trouble with some boys who disagreed with him.
with half an eye on something —(also: with one eye on something) directing one’s attention only partly to smth. (while preoccupied with smth. else):
- I spent the day putting in the web pages with half an eye on the TV.