In a 6 th grade classroom, at the beginning of the unit of polyhedra, a teacher emphasized that it was important and necessary to come to agree on definitions of faces, edges, and vertices because it would help students understand what each other was talking about. Throughout the class, the teacher wrote down students' definitions on the board and asked the students if they agreed with the various definitions she had written on the board.

A student said that a face is a flat surface. Another student suggested that a face is where a corner and a face meet. The second definition was challenged by a student. The student who disagreed on the second definition used counter examples to explain her thinking and provided rationale why she disagreed by saying, “I disagree because…” As the class proceeded, the definition of faces was getting polished to be more mathematically sound. A student suggested, “A face is a surface that is connected to edges and corners of an object.” And another student said, “A face is a smooth surface.” To capitalize on this opinion, the teacher asked students to close their eyes and sweep a surface. The teacher told that when they noticed a change in the surface by running their fingers with eyes closed it, it was the point where a face ended and where an edge was.

Regarding edges, a student said that the edge was the end of the face. Another student said that the edge was a place where two faces were connected. Other definitions suggested by students were; when two faces are put together, an edge divides two faces, edges are the thing that connects two faces, an edge is in the middle of two corners.

On the topic of a corner, students suggested; a corner is the point of a figure, a point is where at least three edges meet, the edges all connect to make the corner.

The discussion of definitions of faces, edges, and corners was recurred when students counted the number of faces, edges, and corners to find out the relationships among the number of edges, faces, and vertices of polyhedra. A student constructed a hexagonal prism with an isosceles triangle embedded inside the hexagon. The student counted the top face as 2 faces arguing that the two shapes were separated by the edges of the triangle and therefore were not just one surface. Students discussed if they counted the number of the face as 1 or 2. It seemed that this happened because students did not understand the concepts of faces, edges, and corners. It is a good teaching moment to draw definitions from students not merely telling them what the definitions are.