Individual differences in strategy use (choice and accuracy) were analyzed. A sample of 362 Grade 6 students solved complex division problems under 2 different conditions. In the choice condition students were allowed to use either a mental or a written strategy. In the subsequent no-choice condition, they were required to use a written strategy. Latent class analysis showed that there were 3 subgroups of students with respect to pattern of strategy choices: primarily using a written strategy (more girls than boys); primarily using a mental strategy (more boys than girls); and using a written strategy on more difficult items but a mental strategy on the easier ones (almost no weak mathematical achievers). Strategy accuracies were analyzed with explanatory item response theory modeling. A between-subjects comparison in the choice condition showed that written strategies were usually more accurate than mental strategies, especially for the weak achievers. A within-subject comparison showed that the performance of students who used mental calculation on a particular item in the choice condition improved if they were required to use a written strategy in the no-choice condition. (Contains 4 tables, 4 figures, and 3 footnotes.)