Correction: An earlier version of this story reported an incorrect range for the amounts of the grants received as part of Race to the Top. This version has been updated.

Five school districts won grants ranging from $10 million to $30 million as part of Race to the Top, the Obama administration’s signature competition for K-12 education, the Education Department announced Tuesday.

The winners of this round of grants were largely rural and Southern.

They were chosen by federal officials from among more than 200 applications and were selected because they had created the best plans to personalize learning, department officials said.

The winners are:

●Clarendon County School District Two, a group of four rural districts in South Carolina

●Clarksdale Municipal School District in Mississippi

●Houston Independent School District in Texas

●Kentucky Valley Educational Cooperative, a group of 18 rural districts

●Springdale School District in Arkansas

Although Houston won one, several other large districts, including Baltimore, Denver and Winston-Salem, did not win grants.

Since 2009, the Obama administration has awarded more than $4 billion in competitive grants as part of Race to the Top competitions. The grants are given to states and local school districts that embrace education policy changes favored by the administration, such as the expansion of charter schools, using student test scores to measure the performance of teachers and administrators, and building complex student data systems.

Funding for the program came from the American Recovery and Reinvestment Act and, as the grants have been awarded, the amount available for each subsequent round has decreased. Last year, the department held its first competition for school districts, choosing 16 winners to share $400 million. The total funds available Tuesday dropped to $120 million to be split among the five winners.

In a call with reporters Tuesday, Education Secretary Arne Duncan said there were more quality applications for the grants than his agency could fund.

The administration says that Race to the Top has spurred bold innovations in education. Critics maintain that while Race to the Top means additional resources for winners, it hurts students in the states and school districts that lost their bids.

The district-level Race to the Top is one of several iterations of the grant program. Other versions include a competition among states and a contest among early learning programs.