CEO Forrest Claypool heralded new efficiencies to keep “cuts away from the classroom” earlier this week when he unveiled Chicago Public Schools’ $5.4 billion in budget recommendations for the upcoming school year that will spend about $232 million less than last year.

But at a time when the reduction of classroom teachers outpaces enrollment drops and per-pupil funding is down from a year ago in the cash-strapped district, several central office departments will see increases in their budgets, including an auditing department that Claypool has bulked up since taking the reins of the district about a year ago.

New departments also have been created, according to CPS’ online budget book.

A new Title I and School Improvement Office will have 12 staffers and a budget of about $2.5 million. The Department of School Quality Measurement will have 14 employees and about $2.2 million. And a new Department of Personalized Learning with eight people and a $2.3 million budget.

The Office of Internal Audit and Compliance, headed by longtime Claypool colleague Andrell Holloway, will rise to $4.4 million compared with $1.18 million one year ago.

Even after counting a central office reorganization performed last fall that moved staff into different departments, Audit and Compliance still plans to spend $300,000 more than the $4.1 million it had by the end of 2016, the documents show.

The human resources department CPS calls Talent also is slated to increase by about 30 people and about $8.2 million. That’s as the Office of Student Health and Wellness is cut about $172,000 from the end of 2016.

CPS’ proposed budget is balanced on paper but depends on a few big ifs — including one from Springfield that requires legislators to pass amorphous “pension reform” by January for $200 million. Another, $31 million, is contingent upon the Chicago Teachers Union going along with a contract proposal they’ve already rejected — prompting CTU president Karen Lewis to begin using the word “strike” again earlier this week.

CPS spokesman Michael Passman said some of the departments that appear to be new are merely rearranged from others, for example, the Title I office.

“The creation of this office does not represent an addition of new staff or additional central office spending; instead it is a realignment of staff previously assigned to the Offices of Accountability, School Support Services, and Grant-Funded Programs,” he wrote in an email. School Quality Measurement came from the old Accountability department.

The auditing department also undertook a top-to-bottom look at district processes and spending. And Talent did increase, he said, but the bulk of that is from transferring staff from other offices and hiring new workers to conduct evaluations of special education teachers. About $626,000 helps implement new labor rules and pays stipends to veteran teachers who coach colleagues, he said.

But that constant shuffle stymies anyone who attempts any independent analysis of the budget, including board members from the parent group Raise Your Hand and CTU staffers — and it’s nearly impossible for ordinary taxpayers.

CTU researcher Pavlyn Jankov said he’s troubled that the ratio of spending on central office to schools and networks has decreased since 2015.

And Raise Your Hand’s Christopher Ball said he and his colleagues have been comparing positions and salaries, suspecting that some CPS work previously done in house now gets contracted out.

“It’s very frustrating process because they keep changing the categories under which central office spending occurs from year to year, it’s very difficult to truly tell whether they’ve made a cut or made a gain,” Ball said. “The magnitude of the [central office] cuts always seems to be much lower than what they advertise.”

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