If someone had videotaped us as we discussed the problem, the images would have shown the
two of us fi rst moving our arms and pencils to form right triangles (outlining the faces and edges
of a cube) and then utilizing a tissue box from the teacher’s desk as a concrete representation of
a prism. We pointed to the lines and vertices formed by the walls and ceiling of the classroom,
“drawing” imaginary lines on the surfaces and spaces. Employing these methods, we were able
to visualize some triangles as two-dimensional shapes on and within a three-dimensional space.