Here's a fun exercise: Next time the Maintenance Department has their monthly meeting (Dining Services, Nursing, Environmental, any Department) have them, without the input of the Department Director, create a goal or mission statement for their group. Depending on the status of the Department, make the goal short-term (Action-related) or long term oriented (Outcome-related).
Some may say this exercise potentially detracts from the organization's mission statement. On the contrary; use this as an opportunity to teach the mission statement and relate the group's chosen Mission with the organization. Kudos to the manager that gets the staff to memorize both. Try printing the Employee Stated Mission at the top of Strategic Plans, a Staff Meeting Agenda, etc. to sustain interest.
The point of the exercise is not only to work towards the chosen goal but also to engage the group discussion on areas that needs improvement.