Two experiments were run to determine how presentation modality and duration influence children’s arithmetic performance and strategy selection. Third and fourth graders were asked to find estimates for two-digit addition problems (e.g., 52 + 39). Children were tested in three conditions: (1) time-unlimited visual, (2) time-limited visual, or (3) time-limited auditory conditions. Moreover, we assessed children’s working-memory updating and arithmetic fluency. Children were told which strategy to use on each problem to assess arithmetic performance while executing strategies, in Experiment 1, and were asked to choose the best strategy of three available strategies to assess strategy selection, in Experiment 2. Presentation modality influenced strategy execution (i.e., children were faster and more accurate in problems under visual than auditory conditions) but only in children with low updating abilities. In contrast, presentation modality had no effect on children’s strategy selection. Presentation duration had an effect on both strategy execution and strategy selection with time-limited presentation leading to a decline in children’s performance. Interestingly, specifically in children with low updating abilities, time-limited presentation led to poorer performance. Hence, efficient updating seemed to compensate for detrimental effects of auditory in comparison to visual and time-limited in comparison to time-unlimited presentation. These findings have important implications for determining conditions under which children execute strategies most efficiently and select the best strategy on each problem most often, as well as for understanding mechanisms underlying strategic behaviour.