Adults shift their attention to the right or to the left along a spatial continuum when solving additions and subtractions, respectively. Studies suggest that these shifts not only support the exact computation of the results but also anticipatively narrow down the range of plausible answers when processing the operands. However, little is known on when and how these attentional shifts arise in childhood during the acquisition of arithmetic. Here, an eye-tracker with high spatio-temporal resolution was used to measure spontaneous eye movements, used as a proxy for attentional shifts, while children of 2nd (8 y-o; N = 50) and 4th (10 y-o; N = 48) Grade solved simple additions (e.g., 4 + 3) and subtractions (e.g., 3 - 2). Gaze patterns revealed horizontal and vertical attentional shifts in both groups. Critically, horizontal eye movements were observed in 4th Graders as soon as the first operand and the operator were presented and thus before the beginning of the exact computation. In 2nd Graders, attentional shifts were only observed after the presentation of the second operand just before the response was made. This demonstrates that spatial attention is recruited when children solve arithmetic problems, even in the early stages of learning mathematics. The time course of these attentional shifts suggests that with practice in arithmetic children start to use spatial attention to anticipatively guide the search for the answer and facilitate the implementation of solving procedures.