The Virginia Plan and the New Jersey Plan were two important proposals that were presented during the Constitutional Convention in 1787. The main disagreement between these two plans was centered on the issue of representation in the federal legislature.

The Virginia Plan was introduced by James Madison, a leading figure in the convention. This plan proposed a bicameral legislature with two houses. The lower house, known as the House of Representatives, would be elected by the people, while the upper house, known as the Senate, would be elected by the lower house. Representation in both houses would be based on population size, which meant that the more populous states would have a greater number of representatives and senators.

On the other hand, the New Jersey Plan was introduced by William Paterson, a delegate from New Jersey. This plan proposed a unicameral legislature with only one house. Each state would have equal representation, regardless of its population size.

The main disagreement between these two plans was rooted in the issue of representation. The Virginia Plan favored the larger states, who stood to gain more representation in the federal government through this plan. The smaller states, however, feared that their voices would be drowned out by the larger states, and therefore, they supported the New Jersey Plan.

This disagreement was eventually resolved through the Great Compromise, which proposed a bicameral legislature consisting of the House of Representatives and the Senate. The House of Representatives would be based on population size, while the Senate would have equal representation for each state. This compromise satisfied both the larger and smaller states, and it went on to become an integral part of the U.S. Constitution.

In conclusion, the main disagreement between the Virginia Plan and the New Jersey Plan was centered on the issue of representation in the federal legislature. While the Virginia Plan favored larger states, the New Jersey Plan sought to protect the interests of smaller states. This disagreement was eventually resolved through the Great Compromise, which led to the creation of a bicameral legislature that still stands as the backbone of the U.S. government.