Ask your students to research the life of a past American president. Encourage them to look into the lives of less well-known presidents whose administrations were nevertheless consequential, such as John Tyler, Franklin Pierce, James Buchanan and Warren G. Harding. Depending on grade level, students can create posters, give oral presentations or write formal research papers on the president they choose.
Have your students investigate the history of the debate over the U.S. Constitution and historical attitudes toward the executive branch. While some founding fathers, like Alexander Hamilton, favored a strong federal government whose power was vested in the executive branch, others, like Thomas Jefferson, opposed centralized authority and feared the abuse of power from the executive branch. Ask your students to participate in a debate over the issue of what powers the executive branch should have and when it should be allowed to exercise them.
Ask your students to look at foreign countries, many of which do not have a branch of government that closely resembles the American executive branch. In the United States, the power of the Executive Branch lies chiefly with the President, who is also the head of state. In countries that have constitutional monarchies, however, such as the United Kingdom and Sweden, the current sovereign rather than the democratically elected leader of the current parliament is the head of state. Have them compare and contrast the two approaches to having a head of state and ask to to write an issue paper where they argue for or against our presidential system.
Have your students research a current member of the president's cabinet or the head of a federal agency. While we tend to think of the executive branch as consisting of the president and the vice president exclusively, there are many others who act in smaller administrative roles. According to the White House's website, more than 4 million people work for the executive branch, if you include those currently serving in the United States armed forces.