While Schools Chancellor Joel Klein often complains that too many city schoolchildren are failing math and English, it turns out his own staff is also struggling with basic skills like spelling, sums, and estimation.

Top Department of Education officials distributed a new preparatory guide this week that is full of mathematical mistakes, spelling errors, and grammatical slipups, as well as formatting flaws.

The errors start on the cover with the title: “Mathematics Planning For Forth Grade.” (The word forth, of course, means “onward in time, place, or order”; the ordinal number corresponding to the number four is spelled “fourth.”)

The mistakes continue inside.

One of the practice questions for fifth-graders asks students to round the numbers 178, 212, and 254 to the nearest hundred and then add them together. The correct answer is 700; the guide indicates that it is 600.

One of the sample questions for seventh-graders asks students to evaluate the expression xy-z+2y if x=3, y=5, and z=0. The correct answer, 25, is nowhere to be seen. Instead, the guide says 24 is what the students should put down.

“It’s kind of laughable, actually, don’t you think? It makes you wonder who’s minding the store,” a professor of mathematics at the Courant Institute of New York University, Sylvian Cappell, said. “While little mistakes are not the issue, it doesn’t inspire confidence about the larger issues.”

He said the city’s math community has offered to help the department when it comes to math education.

“There’s been no responsive interest at all from them,” Mr. Cappell said. “I can only tell you we wouldn’t have made those mistakes.”

Parents, politicians, advocates, and union leaders were equally unimpressed with the education department’s new guide.

“Tweed has no problem with excessively criticizing teachers for failing to meet its picayune mandates, but then it produces a test prep manual riddled with errors and misspellings,” the United Federation of Teachers president, Randi Weingarten, said. “The hypocrisy is stunning.”

She continued: “They could avoid embarrassing things like this if they were more collegial and shared these documents with us, instead of running things in a top-down management style that does not welcome – or want – input.”

The chairwoman of the City Council’s Committee on Education, Eva Moskowitz, said, “You just sort of wonder why they can’t get the most basic things right. Whether it’s being given out to the administrators, the teachers, the kids, the bottom line is it’s got to be a professional work product, and this seems to be far short of that and that’s unacceptable.”

A parent who advocates for reforming the math curriculum, Elizabeth Carson, said she’s not surprised that the guides had so many flaws, given that the city has used flawed tests in the past. But she said that should not be an excuse for being “sloppy.”

“It puts the kids at a disadvantage. It puts the teachers at a remarkable disadvantage,” she said. “It sets the kids up to fail. It sets the teachers up to fail.”

The co-chairwoman of Time Out From Testing, Jane Hirschmann, said, “The standards are so low that even the test prep booklet is inaccurate.”

She said the whole idea of spending money to create a test prep guide seems like a waste of city funds, and that the city should be spending money on improving instruction rather than improving test preparation.

“It’s gotten totally out of hand,” she said. “This is just an example of how out of hand it is.”

The education department e-mailed and handed out CDs of the guides to regional instructional specialists, local instructional superintendents, and math coaches Wednesday night and recalled them within hours. The guides were created internally by the Department of Teaching and Learning, which said the guides didn’t cost any money beyond the salaries of the employees who wrote them.

“We have a clear protocol for review of all materials. In this case, a member of my staff inexcusably failed to follow our protocol, and I have written a letter of reprimand to the person’s file,” the deputy chancellor for teaching and learning, Carmen Farina, said. “We recalled the materials within hours, corrections to the guide will be made, and again will be distributed digitally.”