In this clip the teacher is leading a discussion about what the graph of the situation will look like.
The Box Problem, Clip 1, 2:11
Notice that the teacher is focusing their attention on the quantities involved in the problem. She is allowing them to decide which ones vary and which do not.
When the idea is not brought up by the students, she points out that the cutouts must be squares. She also asks them what would happen if the cutouts were rectangular.
Note that the teacher gives wait time after each of her questions, but she gives the answer if necessary as they are also constrained by the time of the class.
The teacher uses the Explore Box applet in order to help the students imagine the covariation and determine what happens to create a volume of 0.
She also uses the applet to begin to motivate the notion of a maximum volume.
