The present study investigates how children's better strategy selection and strategy execution on a given problem are influenced by which strategy was used on the immediately preceding problem and by the duration between their answer to the previous problem and current problem display. These goals are pursued in the context of an arithmetic problem solving task. Third and fifth graders were asked to select the better strategy to find estimates to two-digit addition problems like 36 + 78. On each problem, children could choose rounding-down (i.e., rounding both operands down to the closest smaller decades, like doing 40 + 60 to solve 42 + 67) or rounding-up strategies (i.e., rounding both operands up to the closest larger decades, like doing 50 + 70 to solve 42 + 67). Children were tested under a short RSI condition (i.e., the next problem was displayed 900 ms after participants' answer) or under a long RSI condition (i.e., the next problem was displayed 1,900 ms after participants' answer). Results showed that both strategy selection (e.g., children selected the better strategy more often under long RSI condition and after selecting the poorer strategy on the immediately preceding problem) and strategy execution (e.g., children executed strategy more efficiently under long RSI condition and were slower when switching strategy over two consecutive problems) were influenced by RSI and which strategy was used on the immediately preceding problem. Moreover, data showed age-related changes in effects of RSI and strategy sequence on mean percent better strategy selection and on strategy performance. The present findings have important theoretical and empirical implications for our understanding of general and specific processes involved in strategy selection, strategy execution, and strategic development.