Previous studies have provided that when learning shapes for the first time, young children tend to use the prototype as the reference point for comparisons, but often fail when doing so since they do not yet think about the defining attributes or the geometric properties of the shapes. Most of the time, elementary students learn geometric properties of shapes only as empty verbal statements to be memorized, without any chance to experience the concepts meaningfully. In the light of it, a sequence of instructional activities along with computer manipulative was designed to support Indonesian third graders in constructing geometric properties of square, rectangle, and triangle. The aim of the present study is to develop a local instructional theory to support third graders in constructing geometric properties of rectangle, square and triangle. Thirty seven students of one third grade classes in SD Pupuk Sriwijaya Palembang, along with their class teacher, were involved in the study. Our findings suggest that the combination of computer and non computer activities supports third graders in constructing geometric properties of square, rectangle, and triangle in that it provides opportunities to the students to experience and to develop the concepts meaningfully while using their real experiences as the bases to attain a higher geometric thinking level.