NEW YORK — A strong start to the U.S. shopping season and hopes for a far-reaching solution to Europe’s debt crisis sent stocks sharply higher this morning.

The Dow Jones industrial average jumped 303 points, or 2.7 percent, to 11,535 at 11:45 a.m. Eastern Time.

The Standard & Poor’s 500 rose 35, or 3.1 percent, to 1,194. The Nasdaq composite rose 88, or 3.6 percent, to 2,529.

A record number of shoppers hit the stores or bought gifts online during the holiday weekend. Thanksgiving weekend is a make-or-break time for many retailers.

For the past six years, Black Friday has been the biggest sales day of the year.

Markets in Europe also are up sharply as leaders there discuss new approaches for containing the region’s debt troubles, including a joint bond issue.