The Virginia Plan and the New Jersey Plan represented two different approaches to creating methods of representation of individual states in the government that was being designed for the new United States.
The Virginia Plan, authored by James Madison, proposed a two-body legislature, a president or chief executive position, a system of national courts, and checks and balances to prevent any one branch of the government from becoming too powerful at the cost of the other branches. In the Virginia Plan, representation of individual states in both houses of the legislature would be in proportion to the population of the states, thus giving states with larger numbers of free residents a larger voice in the government.
The New Jersey Plan, as presented by William Paterson, reflected the opposition of states with smaller populations to the idea that more populous states should be given more representation in the legislature. The New Jersey Plan proposed a unicameral legislature, one body in which each state would have one vote.
The Great Compromise that finally allowed for the successful conclusion of the Constitutional Convention of 1787 adopted features from both of the plans. The House of Representatives used the representation in proportion to population idea presented in the Virginia Plan, while the Senate gave equal representation to every state as suggested by the New Jersey Plan.