Keep the following numbers in mind for the next time a public-sector union official starts lecturing you about social justice.

In Chicago, 85 percent of the roughly 400,000 public school students are either African American or Latino. A similar percentage receives free or reduced-price meals, which means these students live at or near the poverty line: $27,214 for a family of three, in a typical case.

The average public-school teacher in Chicago earned almost triple that amount — $76,000 per year, according to the school district. In contract negotiations this year, Chicago Public Schools offered an average total pay increase of 16 percent over four years.

The Chicago Teachers Union, 26,000 strong, rejected the offer and went on strike Monday, sowing chaos among children and parents.

No one can say how long this walkout will last, but even if it ends tomorrow it has already harmed poor minority children, upon whose education the future of Chicago, and the country, depends.

I cannot describe the moral repugnance of this strike by aggrieved middle-class “professionals” against the aspiring poor. Well, I could describe it, but only by plagiarizing Chicago Mayor Rahm Emanuel’s unprintable vocabulary.

So let’s just say events in Chicago illustrate rather dramatically the contradictions between public-sector unionism and the efficient delivery of vital public services.

They also heighten the contradiction between the Democratic Party’s need to show it can deliver sustainable good government and its dependence on public-sector unions for political funding and get-out-the-vote foot soldiers.

Common sense says there should be some link between compensation and job performance. But the very idea tends to make teachers unions recoil like Dracula confronted with a garlic clove. And so the Chicago Teachers Union is picketing schools that graduate only 60 percent of their students and where fewer than 8 percent of 11th-graders met all four college readiness benchmarks on 2011 state tests, according to the school system.

To his credit, Emanuel decided to shake things up when he took office last year, even if it meant tangling with the teachers union. He rescinded an unaffordable pay increase and called for a 90-minute extension of the school day, which, at six hours, was one of the shortest in the nation. That infuriated the teachers union; a truce was reached when Emanuel agreed to rehire laid-off teachers to handle the extra workload.

But bad blood remains, and beyond prosaic issues of pay and benefits lurks the all-important question of linking teacher job security to student test scores. Chicago Teachers Union President Karen Lewis warns that “this is no way to measure the effectiveness of an educator,” and she griped in a statement about the impact “poverty, exposure to violence, homelessness, hunger and other social issues beyond our control” can have on student performance.

I believe this is what a certain former president meant by “the soft bigotry of low expectations.”

To some extent we are witnessing a quintessentially Chicagoan fight over “clout”: Lewis is determined to show Emanuel who really runs the Windy City, and vice versa.

She has chosen a strategically advantageous moment to make her stand. Emanuel’s time and attention are not fully engaged, since he has just agreed to hit up wealthy donors on behalf of the largest pro-Obama super PAC. Meanwhile, the Obama campaign and, indeed, the entire Democratic fall effort are counting on help from the teachers union and its parent, the American Federation of Teachers. No wonder AFT President Randi Weingarten was pleading for a compromise in Chicago during last week’s Democratic National Convention.

But the outcome matters — a lot. If Emanuel can open a pay-for-performance beachhead in the nation’s third-largest school district, it would send a message across the country. If not, the setback would reverberate well beyond Chicago, too.

Actually, it should be lesson enough that about 400,000 mostly poor schoolchildren, and their parents, and the voters of Chicago generally, are regularly held hostage to closed-door bargaining between politicians and union chieftains — not to mention grander partisan political machinations.

Some wonder why Emanuel doesn’t just give the teachers half a loaf, so the kids can go back to class.

The real question is how things got to the point where the mayor isn’t legally free to drop one of his F-bombs on the Chicago Teachers Union and hang out a Help Wanted sign for new teachers — pay, benefits and work rules to be set by elected officials, in accordance with the public interest, period.