Alex Finkelstein, along with his wife Amy and their two children Emma, 11, and Andrew, 9, hadn’t traveled more than a mile offshore from Menemsha toward Lobsterville on Monday morning when they spotted what they believed was a massive school of fish.

“We thought it was bonito jumping, but then we saw the fins,” Mr. Finkelstein said. When the family pulled up closer, they found themselves surrounded by a pod of dolphins totalling about 150 members, including at least one immature dolphin, or pup, that was about one and a half feet long.

The pod swam around and alongside their boat, The Optimist, for about 45 minutes. The dolphins were so close, Mr. Finkelstein said, that they could have reached out and touched their backs.

“We didn’t, though,” he said. “Because they were blowing out of their blowholes and spraying us. It was really cool for the kids. We could have followed them all day.”

Mr. Finkelstein recorded the encounter and sent the video to the Gazette. When the Finkelsteins parted ways with the dolphins around noon, they watched as the dolphins headed further out into the Vineyard Sound toward the Elizabeth Islands.

“We left and then we caught a really nice striped bass,” he said.