The two events were so unrelated that one might expect them to appear together in a story on the state’s English language arts exam.

This afternoon, critics of the city’s school closure policies gathered for a protest on one side of the Department of Education, while just meters away inside City Hall, Mayor Bloomberg was congratulating I.S. 318’s chess team on their underdog win at last week’s National High School Championships.

The protest outside the Department of Education’s headquarters drew about 40 teachers and students, including many from schools that face a closure vote next week.

Turnout was denser inside City Hall, as Bloomberg and Chancellor Dennis Walcott crowded in for a photo shoot with the I.S. 318 students, who returned from the tournament just in time for the start of annual state tests.

Banter between the students and the officials soon turned to this week’s tests. Several of the students are in eighth-grade and described for the mayor their confusion upon being asked to answer questions about a story called “The Pineapple and the Hare.” The story, an adaptation of a story by the absurdist children’s author Daniel Pinkwater, had flummoxed the students, who said they were not sure how to answer a question about why the pineapple was eaten.

The story has confused students across the city and elsewhere, when it has appeared on other states’ exams, according to parent activist Leonie Haimson, who compiled criticism of the test passage dating back several years on the NYC Public School Parents blog today.

On his website today, Pinkwater offered an explanation for how his story, “The Rabbit and the Eggplant,” wound up in a different form on state tests year after year.

“There are these companies that make up tests and various reading materials, and sell them to state departments of education for vast sums of money,” he wrote. “One of the things they do is purchase rights from authors to use excerpts from books. For these they pay the authors non-vast sums of money. Then they edit the passages according to … I have no idea what perceived requirements.”

The state is in the process of toughening exams to reflect new standards and seeking a different company to produce the tests. City officials said the looming changes would insulate students against similar test passages in the future.

“We strongly support the state’s commitment to improving its tests over time, and we expect to see much more rigor and complex reading passages on next year’s tests,” said Chancellor Dennis Walcott in a statement.

Back at the closure protest, union politics, not pineapples, were front and center. Nick Licarri, who retired after Norman Thomas High School phased out, blamed the UFT’s leadership for not mobilizing its members against school closures. “It’s unfortunate that there are not thousands of people at this demonstration,” he said.

UFT President Michael Mulgrew has railed against turnaround, and union officials have spoken up at individual schools’ closure hearings in recent weeks, as well. But the union did not sign on to today’s demonstration and has not announced plans for a protest at next week’s Panel for Educational Policy meeting. At the February meeting where the panel voted to close or shrink 23 schools, the union’s protest was derailed by competing demonstrations — including one led by the Occupy the DOE movement — in a scenario the union might be hesitant to repeat.

Anti-Bloomberg rhetoric was fierce. But Kevin Kearns, a teacher at Lehman High School, said he agreed with the mayor on at least one point.

“I would agree that they make it up as they go along in many ways,” he said, referring to Bloomberg’s comment from earlier this week about why rumors of 75 school closures next year should not be believed.