21st Century Classroom Innovation Act - Amends part A (Teacher and Principal Training and Recruiting Fund) of title II of the Elementary and Secondary Education Act of 1965 to allow states to use that portion of their part A grant funds reserved for state activities to award competitive grants to local educational agencies (LEAs), charter schools, or consortia of such entities to carry out blended learning projects.

Defines a "blended learning project" as a formal education program that: (1) includes an element of online learning and instructional time in a supervised location away from home; (2) includes an element of student control over time, place, path, or pace; and (3) connects the modalities along each student's learning path within a course or subject to provide an integrated learning experience.

Requires the competitive grant funds to be used for: (1) planning activities, the purchase of digital instructional resources, initial professional development activities, and one-time information technology purchases; or (2) ongoing professional development for teachers, school leaders, or other personnel involved in the project.

Requires each state making such a grant to contribute non-federal funds equal to at least 10% of the grant.

Reduces, from 2.5% to 1.5%, that portion of part A grant funds that states must reserve for subgrants to local partnerships between institutions of higher education and high-need LEAs. (This increases the amount reserved for state activities.)