Overview:  To launch the problem, the teacher reviews the concepts of “perpendicular” and “bisector” with an example of reflecting a triangle to make a kite.  The teacher makes a reflection and connects a point to it’s image across the mirror line.  The teacher asks students to observe     the relationship between the mirror line and the line segment connecting the point to its reflection.  Students quickly notice that the line is perpendicular, and then the teacher prompts them to notice that the line bisects.

Prior knowledge:  The teacher launches the problem with a review of the school mathematics knowledge that students will use to solve the problem.  Students should have previously studied perpendicular lines and bisectors.  However students would not, prior to this lesson, have put together these ideas to form the concept of “perpendicular bisector”.  With his review of these concepts, the teacher makes the core mathematical ideas of the lesson explicit.

Other points of interest:  When the teacher asks students to make observations about the sketch of the kite, the conversation follows an Initiation-Response-Evaluate [IRE] (Mehan, 1979) pattern.  First a student observes that the two lines intersect, which is not the idea that the teacher seems to be looking for.  The teacher illustrates a practice of funneling students’ responses (Anghileri, 2006; Herbel-Eisenmann & Breyfogle, 2005; Wood, 1998) to guide them to provide the responses the teacher is looking for.  Although the teacher elicits the vocabulary of “perpendicular” and “bisector” from students, it is not apparent from the vignette what knowledge students have of this vocabulary.