When his mother, Kiana Ashburn, 32, found the letter buried at the bottom of his backpack, she waved off his pleas to go to the karate camp she had signed him up for. “You need to get a good education so you can get a good job and have a good future,” she told him that afternoon in their sparely furnished rowhouse in the Fordham neighborhood of the Bronx.

She was all the more certain on the Friday before the program started, when the world awakened to a Facebook Live video of an unarmed black cafeteria worker in Minnesota, Philando Castile, bleeding to death in his car after being shot by a police officer.

She often made Jonathan repeat what he was to do if he were ever stopped: “Just do what he says, and like, don’t try to resist,” he recited.

She thought of math as a field that “usually Asians dominate,’’ she said. It would not protect him from police violence, she knew, or the other things she feared. Her brother had spent time in prison.

“But it could act as a buffer,” she remembers thinking.

Ms. Ashburn, a postal clerk who graduated last year with a business degree from Monroe College in the Bronx, left before dawn for work on the first day of camp. Jonathan’s sister, Jasmine, a year older than him, was headed to summer school after dropping off their younger brothers at karate camp. Jonathan walked himself around the corner at 7 a.m. to meet his subway group in what would become a daily routine.

Omar Pineda Jr. was the counselor assigned to escort them, but it was Emyr Willis, 11, who broke the ice. “Hello,” he greeted them with the formality they would come to see as his trademark. “I am the both the emissary and ambassador from my school.”

Thays Garcia, also 11, was the group’s third member.

“I love math,” she said, her face lighting up when asked why she had agreed to spend her summer doing math problems.