watchful

/ˈwäch-fəl/

adjective

  1. not able or accustomed to sleep or rest : wakeful

  2. causing sleeplessness

  3. spent in wakefulness : sleepless

watchful vigilant wide-awake alert mean being on the lookout especially for danger or opportunity. watchful is the least explicit term. vigilant suggests intense, unremitting, wary watchfulness.

idiom

  1. to watch (someone or something) closely

The supervisor keeps a watchful eye on the workers.

idiom

  1. while being watched by (someone)

The students did their work {phrase}under the watchful/vigilant eye of{/phrase} their teacher.