This talk makes use of Lagrange's Identity to provide a bridge between an insightful motivation and an elementary derivation of the method of equal proportions. The method of equal proportions is the current method for apportioning the 435 seats in the U.S. House of Representatives among the 50 states, following each decennial census. We also present some historical comments about the first two methods of apportionments as well as the last two methods of apportionment.