H.R.3606 - Federal Government - To amend the Elementary and Secondary Education Act of 1965 to provide grants for core curriculum development.

Access to Complete Education Act - Amends the Elementary and Secondary Education Act of 1965 to authorize the Secretary of Education to award grants to local educational agencies (LEAs) to promote and strengthen as an integral part of the curriculum one or more of the subjects of music and arts, foreign languages, civics and government, economics, history, geography, and physical education and health.

Gives priority to LEAs that have greatest numbers or percentages of children from families below the poverty line.

Requires grantees to coordinate, to the extent practicable, their programs to promote or strengthen education in such subjects with opportunities provided by public or private cultural entities, including museums, education associations, libraries, and theaters.