He attended Flagstaff High School and Northern Arizona University. After making his debut for the Cubs in the final week of the 1922 season, Grantham became their everyday second baseman in 1923, playing in a career-high 151 games and stealing 43 bases.\n', "

Grantham hit over .300 every season from 1924 to 1931. During the same span, his on-base percentage was .408. He was traded by the Cubs after the 1924 season to the Pirates in a six-player swap that sent future Hall of Famer Rabbit Maranville to Chicago, switching over to first base. With Pittsburgh, he appeared in the 1925 and 1927 World Series. He hit .364 in the '27 Series against what some consider the greatest Major League team of all time, the '27 Yankees.\n", '

In 1930 he hit .324, setting career highs in hits (179), RBIs (99), and runs scored (120).\n', '

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