Freezing temperatures and scattered picket lines marked the first day of Yale’s weeklong strike Monday, as graduate students and hospital workers joined ranks with members of Yale’s two largest unions.

Members of locals 34 and 35, whose numbers were estimated to be in the thousands, picketed around campus throughout the morning with members of the Graduate Employees and Students Organization and unionized workers from Yale-New Haven Hospital. Many striking workers and graduate students also participated in a march from Wooster Square to College Street with the Rev. Jesse Jackson late Monday afternoon as part of the day’s theme — the need for a “social contract” between Yale and New Haven.

Both union and University leaders said 95 percent of the 1,100 members of Yale’s service and maintenance union, Local 35, participated in the job action. But leaders from the two sides disagreed about how many other workers and graduate students participated.

The morning’s pickets garnered attention from several national media outlets, including ABC News, CNN, the Associated Press, The New York Times and Reuters news service.

Union members will continue the strike today, focusing on health care. Picketers will gather outside the School of Medicine around noon. Service Employees International Union President Andrew Stern and SEIU District 1199 President Dennis Rivera will address the group at the corner of York and Cedar streets.

Local 34 President Laura Smith said approximately two-thirds of the 2,800 members of Local 34, Yale’s clerical and technical union, went on strike, yielding the highest participation rate in the union’s history. She said all 150 dietary workers from the hospital and about 1,000 graduate students also took part in the walkout.

Yale spokesman Tom Conroy said about half of Local 34’s members reported to work Monday. He said it was difficult to determine how many graduate students were striking this week.

Conroy said the University functioned “very close to normal” during the first day of the walkout.

He said Yale officials cannot estimate what percentage of workers will show up to work during the remainder of the strike but that the University expects a similar turnout.

“Certainly the expectation is that those who came to work today will come to work the rest of the week,” he said.

In the morning, workers and graduate students formed picket lines around many areas of campus, including Beinecke Plaza and the area of College Street outside Phelps Gate.

Many union members, graduate students, undergraduates and members of the New Haven community also convened on the corner of College and Elm streets around 5 p.m. Monday to participate in a march led by Jackson. At the end of the march, Jackson, local clergymen, city officials and union leaders spoke to a crowd of over 1,000 people about the need to negotiate fair contracts and for University administrators to recognize the right to organize.

Smith said she was disappointed that the unions had to hold a walkout but said she was pleased with the commitment that striking workers have demonstrated. She said the first day of the strike was a “tremendous success.”

“I think I have mixed emotions,” she said. “Obviously, I didn’t want to be out on strike, but certainly I feel wonderful about the response of our members.”

Union members and graduate students will picket in the same general locations today during the late morning and form one large picket line at the medical school to see Stern and Rivera speak, union leaders said.