Four hundred and three 3rd- and 5th-grade Chinese students took the Multiplication Estimation Test or participated in the interview on it, designed to assess their computational estimation performance on whole-number multiplication. Students perform better when tasks are presented visually than orally. Third graders tend to use rounding based while fifth graders tend to use written algorithm based strategies, but boys' and girls' performances do not differ. It is concluded that students often will not estimate simply at the request to estimate if an exact answer is within their mental computation capability, and a two-step process is suggested for helping students decide what route to take when given arithmetic problems. (Contains 5 tables.)