Flexibly spotting and applying shortcut options in arithmetic is often a major challenge for children as well as adults. Recent work has suggests that children benefit in terms of such flexibility from tasks requiring estimation or other operations with quantities that they cannot easily enumerate. Such tasks often require comparison of quantities by fixation and as such necessitate long-range eye movements, e.g. across the whole screen. We tested whether fixation patterns account for transfer from estimation to arithmetic tasks. Conceivably, participants who first solve estimation tasks are more flexible in spotting and applying shortcuts on later arithmetic tasks, because they stick to scanning the screen with long-range eye movements (which were necessary for solving the estimation task). To test this account, we manipulated the location of the marbles in an estimation task so that one group of participants had to make long-range eye movement, whereas another group did not need long-range eye movements to solve the task. Afterwards participants of both groups solved addition problems that contained a shortcut option based on the commutativity principle. We tested whether shortcut usage and fixation patterns in the arithmetic problems were influenced by the variant of the estimation task provided beforehand. The experiment allowed us to explore whether flexibility in spotting and using arithmetic shortcuts can be fostered by applying a prior task that induces flexible looking patterns. The results suggest that estimation tasks can indeed influence fixation patterns in a later arithmetic task. While shortcut search and application is reflected in fixation patterns, we did not obtain evidence for the reverse influence. Changed fixation patterns did not lead to higher shortcut usage. Thus, the results are in line with top-down accounts of strategy change: fixation patterns reflect rather than elicit strategy change.