After being raised in Brooklyn, New York, Blackman attended Kansas State University where he was named the Big Eight Conference Player of the Year and All-American, he was a three-time unanimous All-Big Eight selection, and he was three times named the Big Eight Defensive Player of the Year. He scored 1,844 career points, the second-highest total in K-State history.

Blackman was drafted by the Dallas Mavericks in the first round (9th overall) of the 1981 NBA Draft. In eleven seasons with the Mavericks, Blackman was named to the NBA All-Star Team four times and played on six Maverick playoff teams. Blackman scored 16,643 points and 6,487 field goals with the Mavericks, both of which remain team records. His number 22 was retired by the Mavericks on March 11, 2000.