Rice began his career at Mt. Carmel as a running back. The roster was so deep that Coach Frank Lenti moved Simeon to tight end and defensive end before his junior season. Simeon fought the move, purposely dropping passes and missing tackles in practice. He still did not see much action in games. Before his senior season, Coach Lenti had a talk with Simeon and told him there was still time to be great at football, but he had to accept that he was better suited for defense. His senior season, he got better with every game, starting with the first game of the season against Joliet Catholic and their star running back, Mike Alstott. In the state championship game, with Mt. Carmel trailing, Simeon had a sack that caused a turnover which gave the team the momentum to mount a comeback victory. Throughout the season, Coach Lenti advocated for schools to recruit Simeon, but few listened. Simeon wound up at the University of Illinois for college.