Ever since it began doling out money per student for school budgets a few years ago, Chicago Public Schools officials have blamed most teacher layoffs on enrollment drops, especially the round of pink slips after the release of each year’s budget.

CPS said the layoffs earlier this month of 494 teachers and 492 support staff of were part of a “normal annual staff movement between schools” because when enrollment drops, so does funding to its schools, and with fewer students, a school doesn’t need as many staffers. As the Chicago Teachers Union criticized the layoffs, the district also pointed to 1,000 vacancies that still need filling systemwide.

A Sun-Times analysis of the layoffs found numerous examples of a disconnect between enrollment patterns and the number of teachers and other staff let go.

In fact, several schools projected to gain enrollment laid off multiple staffers — and will lose staff overall, something of a paradox under the student-based budgeting model.

Despite plans to hire new staffers — whose qualifications may better fit the schools’ plans for the upcoming year — some schools set to pickup students still will have fewer teachers and support staff than last year.

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Bowen High School laid off three of the 30 teachers it had as of the end of the school year and at least two support staff even though it’s supposed to pick up 34 students. The South Chicago high school planned to hire back two teachers and one aide, so it still will be down two staffers. Walter Payton College Prep is gaining 114 students but laid off a teacher and has three fewer teachers than in June.

Even more schools laid off a higher proportion of staff than enrollment they’re projected to lose.

Lowell Elementary School is losing just 21 kids of 429 — almost 5 percent — but let go of 4 out of 42 teachers — 9.5 percent, CPS numbers show. Franklin Fine Arts Center Elementary may lose just four students, about 1.1 percent, but lost three out of 31 teachers and also will suffer a net loss of 20 percent of its staffers.

Juarez High School laid off 5 percent of teachers — six of 115 — after losing 1.4 percent of students, or 24 of 1,686, and will start this school year with four fewer teachers than last year. Mollison Elementary also laid off four of 32 teachers after losing 34 of 385 students — and will start school with six fewer teachers than in June.

The calculations used CPS’ school-by-school budget projections, their layoff list from Aug. 5, and a June count of teachers and support staff known as ESPs also provided by the district.

Members of the parent group Raise Your Hand noticed some of the discrepancies, saying the budgeting process makes it hard for parents and teachers to easily understand what’s happening.

Wells High School, for example, is slated to lose just 31 students from its population of 461. Yet 10 teachers — of 43 at the end of last year — were laid off.

“It’s unclear what’s going on in some of these situations,” director Wendy Katten said. “It does not make sense.”

CPS spokeswoman Emily Bittner said some layoffs resulted from program changes, so the net change in staffing might differ from how many were laid off.

For instance, the layoff of four teachers at Disney II Magnet School may have surprised the school community about to add 12th grade and an estimated 127 students. But the North Side magnet is closing its Arabic program, and visual arts staff was reduced to accommodate a new part-time music teacher, according to its Local School Council. A part-time PE teacher also was let go.

CPS said that’s not the final count; the school is adding staff such as the new music teacher, for example, and a grant-funded technology coordinator. CPS-provided numbers show the school will net seven more teachers and two more support staff.

But Wells will still end up losing four teachers since June.

Schools have less per-pupil money to spend now than last year. Student-based budgeting amounts for this entire year were pegged to a cut imposed last February. And schools used surplus state money for poor kids to plug last year’s cuts, leaving less in the bank.

Meanwhile, the district has tried to redistribute federal money for poor children and an $8 million pot for “program support” where schools have shrunk to tiny sizes or had enrollment suddenly plummet. It also moved federal money aimed at keeping class size small to the worst-off schools.

And a few schools did better with staff than their enrollment might indicate.

Foreman High School pink-slipped nine of 85 teachers, including English teaching veteran Melanie Lopez, who started at Foreman in 2004 when enrollment topped 2,000.

“That’s just this year,” she said. “Last year we were losing people also.”

Lopez said she’ll return to Foreman because a colleague died. But the school also let go security guards, aides and their “copy queen” because of projected triple-digit enrollment declines.

“For us to be this low is devastating,” Lopez said. “We’re losing so many good teachers, it’s ridiculous.”