Participants carried out single-digit additions, involving either 7 or 11 numbers, as fast and as accurately as possible. These sums were interpolated among other tests that measured numeracy, working memory capacity, visuo-spatial processing speed and attention switching, in such a way as to permit the presentation of the sums twice, once presented on a piece of paper and participants placing their hands flat on the table and once as a set of manipulable tokens. Efficiency was slightly better in the static condition for easy sums but declined substantially relative to the interactive condition for hard sums. Regression analyses revealed that in the static condition 22% of the variance in efficiency was explained by numeracy and working memory capacity, but 45% by numeracy, working memory capacity and attention switching skills in the interactive condition. Verbal protocols revealed that paths to solution and arithmetic strategies were substantially transformed by interactivity.