The majority of the Building Gifts are divisions of the wood cube from Gift 2. Gift 3 divides the two-inch cube in 8 smaller cubes, Gift 4 changes the form slightly by dividng into 8 oblong bricks (1" x .5" by 1"). Gifts 5 introduces the triangular prism, while Gift 6 offers a variety of rectilinear shapes. The triangular prisms of Gift 5 are dividng the cube in half diagonally while some shapes of Gift 6 divide the oblong shape in half lengthwise (a 1" x 1" x .5" "cap") and widthwise (a .5" x 1" x .5" "column").
The various shapes offer a wonderful variety of architectural possibilities for building but also imply porportional relationships that useful for understanding geometry and arthimetic. Gift Play is traditionally divided into three categories, Forms of Knowledge (e.g. math), Forms of Beauty (abstract patternmaking) and Forms of Life (building models of real world objects).