Wazina Zondon’s 10th-grade class was playing a game about birth control. The students picked a method while Ms. Zondon left the room. When she came back, she had to guess what it was.

“Am I a barrier method?” asked Ms. Zondon, a family life and sex education teacher at the Urban Assembly Institute of Math and Science for Young Women in Downtown Brooklyn. “Are hormones involved?”

After a few more questions, Ms. Zondon guessed correctly: an IUD. Other options included condoms, the birth control patch and abstinence. The students had learned about all of them earlier in the class, including how to use them properly and what, if any, side effects they can cause.

Ms. Zondon’s class offers something advocates say is all too uncommon in New York City: comprehensive sex education. Since 2011, the Department of Education has required that all middle and high schools teach sex education as part of health class. But the requirement came with little enforcement or oversight and compliance has been spotty.

A bill before the City Council, backed by Planned Parenthood of New York City and a number of other reproductive health and youth advocacy groups, would create a task force to study whether and how sex education is taught and make recommendations for improvement.

In 2016, about 43 percent of eighth-graders in New York City had never taken a semester of health class, according to data released by the Department of Education. Nearly all graduating 12th-graders had taken health, but that doesn’t always include sex education, which the department does not track. Moreover, about half of the city’s high school students take health in their junior or senior year, which experts say is far too late to begin learning about healthy sexuality. The average girl in the United States begins dating at 12 and a half years old and the average boy at 13 and a half, according to the American Academy of Pediatrics.

Many reproductive health advocates say students should learn not just about avoiding sexually transmitted infections and unintended pregnancy, but also about consent, a variety of gender identities and sexual orientations, healthy relationships and making informed decisions about sexual behavior.

“Any great sexual and health education program should be focused on helping young people identify what their goals are and then how they can advocate for themselves to achieve those goals,” said Louise Langheier, the chief executive of Peer Health Exchange, a program in which college students teach sexual health lessons to high school students around the country.

Students at the Urban Assembly Institute get sex education every year, starting in the sixth grade with lessons on puberty and anatomy, as well as things like crushes and the emotional changes of adolescence, and continuing in later years with information on sexually transmitted infections and contraception. At all levels, the students learn about having healthy relationships, not just with romantic partners, but with parents and friends, and about different gender identities and sexual orientations. “L.G.B.T. identity is woven in and normalized throughout the entire school year,” Ms. Zondon said.

The Urban Assembly Institute and about five other schools in the city use the Carrera Adolescent Pregnancy Prevention Program, which combines sex education with financial literacy lessons, career training and mental and physical health care. A 2002 study found that girls in the program were significantly less likely than other girls to have had sex or gotten pregnant. The program did not have a significant effect on boys’ sexual behavior. More recent evaluations have found higher rates of condom use among student participants compared with other teenagers.

At other schools in the city, the content of sex education varies widely. The Department of Education offers a free health curriculum that includes lessons on relationships and gender as well as information on condoms and testing for sexually transmitted infections. But schools are not required to use it, and the department does not track what curriculums they use.

Ashley Vasquez, 17, a peer educator with the Teen Outreach Reproductive Challenge program, said her eighth-grade health teacher at P.S. 212 in the Bronx told students to use condoms, but didn’t explain how.

In a recent survey by the Sexuality Education Alliance of New York City, a coalition of teachers, students and health experts, 38 percent of students in grades six through 12 who had received sex education had not learned how to put on a condom. Forty-three percent had not learned about gender identity and 38 percent had not learned about consent.

“Many schools are overburdened with testing,” said Councilwoman Laurie Cumbo, one of the sponsors of the task force bill, which is expected to come to a vote later this year. Sex education, for which there are no state tests or reporting requirements, can fall by the wayside.

Additionally, of more than 15,000 instructors who taught health in the city last year, only 153 were licensed in health. (About 12,000 were elementary schoolteachers, who typically teach multiple subjects and are unlikely to be licensed in health.) “If people aren’t educated around the pedagogy of sex education, they can talk in out-of-touch, fatalistic or inaccurate terms,” or shame students for their sexual behavior, said Francisco Ramirez, the vice president for education at Planned Parenthood of New York City.

School administrators sometimes oppose lessons related to sex. At one middle school, said Mr. Ramirez, an administrator objected to a video describing reproduction shown by visiting instructors from Planned Parenthood. The instructors were not invited back.

Parents are sometimes initially uncomfortable with lessons on gay, bisexual or transgender identities, said Lindsay Fram, a curriculum development coordinator at the Children’s Aid Society, which administers the Carrera Program. But “mostly people want their young people to have the knowledge and skills they need to make healthy decisions,” Rachael Peters, the New York executive director of Peer Health Exchange, said. In a 2009 survey of registered voters in New York State, 85 percent wanted sex education to be taught in schools.

The Department of Education does not oppose the creation of a sex education task force, but at a hearing on the task force bill last month, Elizabeth Rose, the deputy chancellor for operations, questioned whether it would be possible to review how sex education is taught at all of the city’s more than 1,500 schools, and argued that the task force should not be charged with examining the department’s health curriculum.

Councilwoman Cumbo, however, said the task force would provide a much-needed “extra set of eyes” on sex education in the city. She is optimistic that the bill will pass.

“My goal is to continue to do this work until H.I.V. and AIDS and healthy relationships and reproductive health are taken as seriously as biology, chemistry and mathematics,” she said.