Hey, what's that shot of an airplane emblazoned with Donald Trump's name doing in an Obama campaign ad criticizing Mitt Romney on education?

The commercial, which the Obama campaign says will run in the pivotal battlegrounds of Ohio and Virginia on Thursday, is officially about school class size. It hits Romney hard for saying that class size is "irrelevant" to the quality of education. (The former Massachusetts governor has said that smaller class sizes alone won't fix American education, and that smaller class size in Massachusetts was not a reliable predictor of performance.)

And the ad accuses Romney of embracing a government spending plan that would cut education spending by 20 percent. In a statement accompanying the ad, the Obama campaign charged that the Republican's approach would "risk as many as 65,000 educators' jobs," and that "denies what every parent knows: Class size matters, education funding matters, and most of all, teachers matter."

The commercial, which stars a middle-aged couple, wraps up with "Caroline" saying of Romney: "These are all issues that really he personally cannot relate to. To be able to afford an education, to want the very best public education system for your children."

At which point, Romney is shown coming out of his campaign's airplane—with a parked "TRUMP" jet nearby in the background. Message: Mitt Romney is rich. Like, really rich. Like, out-of-touch rich. It's a favorite theme of the Obama campaign, which has painted the election as a contest between a Democratic champion for the middle class and a Republican out to help the wealthy.

At a campaign rally in Columbus, Ohio, on Tuesday, for example, the president mocked Romney for saying that young people should consider borrowing money from their parents to pay for school or start a business.

"Not everybody has parents who have the money to lend. That may be news to some folks, but it's the truth," he said, to laughter from the crowd.

Asked about the new ad, the Romney campaign said it "puts him [Obama] directly at odds with his own education secretary, who has promoted teacher quality—not class size—as the most important factor in a good education."

"President Obama and his campaign have put misleading and hypocritical attacks ahead of a real discussion about education policy," said spokeswoman Amanda Henneberg. "As president, Mitt Romney will pursue genuine education reform that puts parents and students ahead of special interests and gives every child a chance to succeed."