Abstract: A changeable grid system kit for constructing three-dimensional toy and scale model designs, including a base component fabricated of a tough, resilient material, slots formed in the top face of the base, and slats which are insertable into the slots. The invention is designed to ensure that there is little or no loss in the tight fit between the slats and the base material after repeated insertion and removal of the slats. The base material is selected so as to avoid fracturing or splintering caused by repeated use or incidental contact. One such material is a closed-cell crosslinked polyethylene foam. In one embodiment of the invention, the base component is placed vertically such that the slats extend from the slots to form quasi-horizontal surfaces. In this orientation the present invention may be used as an educational tool to illustrate such physical principles as gravity, friction, and the like.