Next week, city schools will add a 37 1/2-minute period for struggling students and chop the regular school day by 10 minutes four days a week. At the top-performing schools with few failing students, parents are complaining that their children are being shortchanged.

“There’s no reward. The kids who do well get a shortened school day,” the chairman of the chancellor’s Parent Advisory Council, Tim Johnson, said.

The Department of Education negotiated the extra time, intended to bolster the lowest-performing students, as part of the most recent teacher contract. Mayor Bloomberg and Schools Chancellor Joel Klein have hailed the contract as a victory that Mr. Klein says will “boost our children’s chances of academic success.”

Letters went out last month to about 300,000 students – or almost one-third of the total students system wide – identified as needing more help. Another 40,000 students were invited to voluntarily attend the sessions that at most schools will be held at the end of the school day on Monday through Thursday.

So far, the loudest grumbling about the added time has come from parents who say that it will throw their delicately calibrated schedules out of whack and make coordinating multiple school pickups even more of a headache.

But now some parents whose children are not included in the extra tutoring are complaining that the 10 minutes of lost class time adds up to five lost days of school a year. At a meeting on Monday night, parents in District 2 – including the strong schools on the Upper East Side, Midtown and Lower Manhattan – vented their frustration, arguing that their children would receive about 18 days less of school than children assigned to the 37 1/2-minute extra sessions.

“There were parents who called the day the letters came out complaining that they didn’t get a letter – they were looking forward to the small class attention,” a mother at the Lower Lab School on Third Avenue and 95th Street, Bijou Miller, said.

The percentage of students achieving at grade level or higher at that school is almost double the city average.

Under the contract negotiated with the United Federation of Teachers, the sessions are capped at 10 students to a teacher, so space is limited. The UFT initially asked that extra time be spread throughout the day for all students and pressed the city to wait until September to implement the sessions.

“I’m very concerned that a majority of kids are losing out on class time as a result of this agreement,” the PTA president at P.S. 234, on Chambers Street, Kevin Doherty, said.

Only 56 of the nearly 700 students at P.S. 234 are required to attend the classes, though an additional 132 students were invited to attend. According to guidelines set by the Department of Education, children who score 1 or 2 out of 4 on the math and English standardized test must attend. Almost no students there scored a 1, the lowest level, and only 21 scored a 2.

For the lower grades where students don’t take standardized tests, it is up to the teacher and principal’s discretion to decide which pupils would most benefit from the extra attention.

The principal of the school, Sandra Bridges, said she could foresee the problem of parents being concerned that their students were being shut out, but added that increased school time could help everyone.

“There’s a saying that you can only move as fast as the slowest person,” Ms. Bridges, said. “If you bring everyone up to speed, the class can move quicker.”

Some top performing schools like East Side Middle will use the extra periods to offer special enrichment programs like forensic science. Other schools will offer art, music, and Spanish culture programs.

“This is a powerful opportunity,” the schools chancellor, Joel Klein, said yesterday in an e-mail. He said that with the two extra days added to the school year in September for all students, struggling students will receive the equivalent of three additional weeks of school a year.

“With 150 extra minutes of help a week, countless children at risk of falling behind will have another powerful push that will help them move to the next grade fully prepared to succeed. Under this new program, stronger students will lose 10 minutes of instruction a day, but I do not think that is a significant setback. It simply moves strong students back to the 6-hour, 20-minute school day that was the norm until just two years ago,” he said.

The school day was lengthened by 10 minutes as part of the prior teacher contract. The Department of Education created the 37 1/2 minute sessions by adding those 10 minutes to the 20 minutes a day negotiated in the most recent contract for a total of 150 minutes divided among four days.

At about 100 schools, the extra time will be used in either two 75-minute sessions or three 50-minute periods, instead of the four 37 and a half minute sessions.

The additional busing for the sessions is expected to cost the city about $24 million from now until June.

At some of the lowest performing schools in the city there are not enough slots for all the failing students.

“It’s kind of sad,” a parent and advocate with Insideschools.org, Clara Hemphill, said. “In the rich neighborhoods, where most of the kids are doing well, there is an opportunity for enrichment like a geography class or forensic science and in the poorer neighborhoods where a lot of kids are scoring below grade level the teachers won’t be able to serve everyone who needs it.”