When it comes to basic math, Chicago Public Schools appears to have a problem counting schools.

A $7 million problem, to be exact.

That’s how much more CPS has spent than anticipated on a contract because it failed to count all the schools that needed to be cleaned.

It’s the latest wrinkle in a controversial contract to privatize custodial management with Aramark, which has faced sharp criticism for failing to keep schools clean.

Aramark was supposed to save CPS $18 million this year. But the district understated the square footage that would need cleaning in its request for proposals, spokesman Bill McCaffrey said, at a cost of $7 million over the projected $64 million CPS expected to spend this year.

That’s partly due to CPS miscounting some administrative offices, school branches and district stadiums, McCaffrey said. And then someone forgot to count entire schools, he added, but he was unable to say how many.

An Aramark spokeswoman quantified the undercounted space at 3.2 million square feet.

Budget documents show that CPS expected to spend $64 million in the first year of the contract, but has already been billed for more than $85 million over 11 months.

Chief Administrative Officer Tim Cawley sold the $260 million Aramark deal to the Board of Education and the public by saying it would free up principals’ time, result in cleaner schools and save the cash-strapped district millions of dollars. Some of the savings was to come from layoffs of hundreds of custodians.

But the district was on the hook for some $20 million more to Aramark than it promised, essentially wiping out the $18 million Cawley said the district would save in its first of three years, as first reported by WBEZ.

McCaffrey said the contract got off to a bumpy start. Problems rolling out the new managers at schools led Aramark to keep custodians targeted for layoffs at schools for several extra months — and that led to another $7.4 million in additional costs.

“As with any new contract, CPS is negotiating with its vendor to reduce costs,” McCaffrey said.

McCaffrey said another $4.5 million sent to Aramark was a wash. CPS is supposed to employ 825 of its own custodians but fell about 100 short every month last year, so Aramark made up the difference in staff, he said. That was money CPS didn’t pay directly to the 100 custodians, he said, insisting CPS still will save $12 million next year and the year after.

Aramark spokeswoman Karen Cutler said CPS also offered “unplanned” early retirement and buyout packages to some of the janitors targeted for layoffs. She also stood by the quality of Aramark’s services, saying schools were cleaner than before the Philadelphia-based company took over.

Within months of Aramark managing school janitors last spring, principals complained about filthy conditions at schools that weren’t cleaned over the summer, and logistical problems that took more of their time, not less. Parents turned up to Board of Education meetings describing vomit that sat on school carpets, and trash that wasn’t removed nightly. Photos obtained by the Sun-Times showed dead vermin at one Southwest Side school.

Clarice Berry, head of the Chicago Principals and Administrators Association, has called for the massive contract to be canceled because promises of cleanliness and efficiency have not come to pass.

She repeated that call Tuesday.

“They have not kept to the terms of the contract, and it should be voided and we mean immediately,” Berry said.

CPS “claimed if they did this and made all this incredible changes that have wrecked havoc on our schools, they’d save money,” she said. “The incompetence of this contract is epic. Heads need to roll at CPS.”