Final answer:
The unwritten constitution includes elements such as the President's Cabinet, traditional term limits prior to the 22nd Amendment, the State of the Union address, and the use of executive agreements for foreign policy.
Step-by-step explanation:
One aspect of the presidency that is part of the unwritten constitution is the establishment of the President's Cabinet. The U.S. Constitution does not explicitly mandate the formation of a cabinet; it's a conventional practice that began with George Washington and has been followed by subsequent presidents as a means of organizing the executive branch.
Additionally, the number of terms a president served was traditionally limited to two, as per precedent set by George Washington, until the 22nd Amendment officially limited presidential terms. Another traditional element is the President's annual State of the Union address to both houses of Congress, an occasion for the president to outline policies and propose new legislation, which has become a fixture in the political landscape despite not being explicitly required by the Constitution.
A more recent historical practice is the use of executive agreements by presidents for foreign policy, which allows an easier way to negotiate agreements with other countries than the treaty process that requires Senate ratification.