This paper reports on children’s responses to a tangram task. The task was designed, based on the draft specification of the primary mathematics curriculum, to facilitate children’s exploration of shape properties and their engagement in mental and physical transformations of tangram pieces. The task was enacted with three cohorts of children from first and second class. Analysis shows some children’s concept images of squares to be limited and their thinking dominated by prototypical geometric images. This research is pertinent in the context of the proposed changes to the Shape and Space strand of the primary curriculum.