DETROIT — Two former Detroit principals will spend time in prison for taking kickbacks from a vendor in a scheme that defrauded the city’s public school system of $2.7 million.

Ronnie Sims was sentenced Wednesday to one year and three months and Nina Graves-Hicks to a year in prison.

Along with vendor Norman Shy and a district administrator, Sims and Graves-Hicks are among 12 principals charged in the scheme. Prosecutors say bogus invoices were submitted for chairs, paper and other supplies. School employees received gift cards, cash and checks.

Sims took more than $58,000 from Shy, while Graves-Hicks received more than $27,000 in gift cards.

The government says Shy paid out about $900,000 in kickbacks. He was sentenced Tuesday to five years in prison. Ex-administrator Clara Flowers was sentenced to three years.