Six Bay Area counties announced even more restrictive shelter-in-place orders Tuesday — including limits on how many people can attend a funeral and directives to close golf courses, playgrounds, dog parks and tennis courts — in an effort to further slow the regional coronavirus outbreak.

The new restrictions, which take effect at 11:59 p.m. Tuesday and extend the stay-home order until at least May 3, were issued the same day the state superintendent told county officials that California schools should not reopen this school year, according to a letter obtained by The Chronicle. Though the superintendent cannot order schools closed, his guidance will almost certainly mean all campuses stay shuttered through the end of the school year.

The announcements came even as public health and other experts say that sheltering in place appears to be working, both in the Bay Area and across the state. The number of new cases reported daily is still growing, but not nearly as dramatically as in New York and other places with explosive outbreaks. And the Bay Area so far is not seeing an alarming surge in people needing hospital care.

But more time and more extreme social distancing — along with closing loopholes that allowed people to keep gathering — are necessary to prevent a health care crisis in the coming weeks, Bay Area health officers said Tuesday.

“Maybe in the last day or two we think we’re seeing a little bit of a slowing. I say that very, very cautiously,” Dr. Sara Cody, the Santa Clara County health officer, said at a news conference in San Jose. “I believe (shelter in place) is starting to bend the curve. But it’s not enough. And it hasn’t been in place long enough. So we need to keep at it.”

School authorities, teachers and parents had expected an announcement that California schools would remain closed. But the letter sent Tuesday finally ended speculation. Superintendent of Public Instruction Tony Thurmond said in the letter that education, in the form of distance learning, would continue even as campuses remained closed.

The new shelter-in-place restrictions involve six counties: Alameda, Contra Costa, Marin, San Francisco, San Mateo and Santa Clara. These were also the first in the nation to institute shelter-in-place orders on March 17. A few days later, Gov. Gavin Newsom ordered a statewide shelter in place, and other states have instituted similar policies.

Sonoma County announced Tuesday night that it extended its shelter-in-place order, along with similar new restrictions. The Solano County health officer said Monday that he extended a local order to April 30, but without tighter restrictions. Napa County officials said they are reviewing their directive.

Tuesday marked two weeks since the Bay Area orders involving the first six counties went into effect, and there are early signs that they have already helped slow down the local outbreak. The Bay Area had 2,372 cases as of Tuesday, roughly double the number of cases one week ago. Statewide, there were 8,530 cases — a doubling over just five days.

That’s concerning, but in New York — which reported more than 75,000 cases as of Tuesday — the count doubled every two to three days last week. Though the New York outbreak appears to have slowed somewhat, many hospitals already are overwhelmed.

The Bay Area and California may avoid that fate, public health officials said Tuesday, but it’s too soon to guarantee that. And they’re worried that the case counts are still climbing at a steady pace. In the two weeks since the shelter-in-place orders took effect, cases in the Bay Area increased sixfold.

Some counties have seen much more dramatic increases — Alameda County shot from just 15 cases to more than 300. So far, the hospitals are not overrun, public health officials said. But they’re still expecting rising case counts that will test the regional health care capacity.

Newsom said during his daily coronavirus update Tuesday that it was still too early to tell what kind of impact stay-at-home orders were having statewide, but social distancing was buying time to prepare the health care infrastructure for an expected surge of patients. He stressed that the number of new COVID-19 cases and hospitalizations was still rising by double-digit percentages each day, which is in line with the state’s estimate that the virus will peak sometime in May.

“No question, we are not out of the woods yet. By no stretch of the imagination should people think that California is overly confident at all,” Newsom said.

In Santa Clara County as of Tuesday, 152 people were hospitalized with confirmed cases of COVID-19, the disease caused by the coronavirus. Another 90 were suspected of being infected but had not yet tested positive, officials said. The county has 1,475 hospital beds in total. Fifty-six COVID-19 patients were in intensive care, with 300 total ICU beds in the county.

“The main issue here is to try to flatten the curve, so to speak. Make sure the capacity and ability for our health system to deal with the very critically ill (COVID-19) and other patients is preserved,” said Santa Clara County Executive Jeffrey Smith at a news conference.

The new directives extend the earlier orders by nearly a month. The tightened restrictions include widespread closures of recreational areas, including public basketball and tennis courts, playgrounds, dog parks, picnic areas and golf courses. Funerals must be limited to 10 people.

Businesses that have been allowed to stay open, such as grocery and hardware stores, must put in place practices by April 3 that allow for greater social distancing and increased cleanliness. Employees may have to undergo daily checks for symptoms, for example. Stores will be required to limit the number of customers allowed inside. Objects like pens, payment keypads and shopping baskets that customers share must be disinfected after every use.

The restrictions are partly a way to close loopholes that public health officials have identified after two weeks of sheltering in place. Many beaches and parks already had been closed due to large crowds gathering, and many cities had shut down playgrounds and similar recreational areas where people gather.

More Information New restrictions for the Bay Area People may no longer use playgrounds, dog parks, public picnic areas and similar recreational areas. They will be closed to public use. People may no longer use public recreational facilities such as golf courses, tennis and basketball courts, pools, and rock walls. These facilities must be closed. Sports requiring people to share a ball or other equipment must be limited to people in the same household. Essential businesses that have continued to stay open, such as grocery stores, must develop a social distancing protocol before April 3. Most construction is prohibited. Funerals are limited to no more than 10 people. Essential businesses that continue to operate must scale down to their essential component only. Keeping kids busy With nearly 6 million children in California forced to stay home during coronavirus school closures, keeping them occupied and learning can be a challenge. Public, private and nonprofit agencies offer a wide array of free resources for educators and families. Common Sense Media: The nonprofit, which teaches digital literacy to kids and families, gives guidance on what to watch or read, online resources for learning at home, insight on COVID-19 to help kids process what’s happening, and stress-relieving activities. commonsensemedia.org Khan Academy: The online learning company is a one-stop shop for short videos and other resources on thousands of topics and school subjects for all grades and college levels, including SAT prep and AP coursework. khanacademy.org Exploratorium: The San Francisco hands-on science museum offers an array of science activities, including a collection of articles, activities and videos on the coronavirus. exploratorium.edu/learn PBS Kids: The public broadcasting division for children has educational games and videos for the younger set. pbskids.org Prepared Parents: Charter school chain Summit Schools is making resources available for parents to help children set routines and create a learning plan. https://preparedforsuccess.org/covid19/ Rock and Roll Hall of Fame: The Cleveland museum is providing access to a range of content for all grades focused on social studies, music, science and more. Some topics include music and civil rights and the role of the drummer in a band, for example. https://edu.rockhall.com/ Reading Rockets: The nonprofit offers support and resources for literacy and reading. readingrockets.org Raddish Kids: This subscription service is offering families free recipes, cooking videos, at-home cooking camp curriculum and daily “cookalongs.” raddishkids.com — Jill Tucker

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On Tuesday, Marin County authorities said that deputies will soon start fining or arresting people who refuse to stop congregating with others. The Sheriff’s Office said authorities have received dozens of calls a day reporting violators.

Santa Clara County officials said they had received 2,000 calls last week to a hotline for reporting individuals and companies violating shelter-in-place orders. In Alameda County, Dr. Erica Pan, the health officer, said that while many businesses that stayed open have been doing their best to encourage social distancing, some have not.

“So we’re making that a requirement,” Pan said. “From a public health perspective, we are trying to balance this. We certainly are not looking to be a police state by any means, but we do want us all to do our part in preventing this spread. It’s a fine line we’re always trying to walk.”

A caption in an earlier version of this story misspelled the name of a student and misidentified her school. She is Juliet Schoenberger and she attends Oakland’s Claremont Middle School.

Staff writers Alejandro Serrano, Alexei Koseff and Anna Bauman contributed to this report.

Erin Allday and Jill Tucker are San Francisco Chronicle staff writers. Email: eallday@sfchronicle.com, jtucker@sfchronicle.com Twitter: @ErinAllday, @JillTucker