Cross Sections of Clay Solids.

This geometry exercise for intermediate and junior high school students has three goals for students: (1) to create three-dimensional clay figures; (2) to think in three dimensions; and (3) to develop vocabulary. Working individually from pictures, students first construct geometric solids out of clay. Second, they attempt to visualize what happens when a solid is sliced at a particular location and angle. The type of solid and how it is sliced will determine the plane figure that will result trapezoid, ellipse, and so on (see fig. 1). Third, students develop a geometry vocabulary by naming the solids they construct. For example, a cube is identified as a hexahedron; a doughnut is a torus. More important, students are asked to name or describe the cross section formed. Since they are not given the correct vocabulary, they must seek it out or develop it on their own. They will find that the terms rectangle and square are not adequate to name all four-sided polygons. In addition to these three objectives, students are given experience in forming hypotheses and then testing the correctness of their ideas. They try to predict the plane figure that would be formed by sectioning a solid; then they test their predictions by slicing the solid and recording their hypotheses and conclusions in a table (see sheet 1).