Overview:  In this launch the teacher performs a review of relationships between angles in pairs of parallel lines cut by a transversal.  The teacher begins by drawing a diagram on the board of a pair of parallel lines intersected by a single transversal.  The teacher asks students to recall the names of pairs of angles found in such a diagram.  A student suggests corresponding angles, and the teacher labels the angles with numbers and asks students to call out different pairs of corresponding angles.  The class follows a similar pattern of conversation for same-side interior angles and alternate interior angles.  The teacher reminds students to use the transversal as a reference for describing the locations of angles in the diagram.  The teacher tells students that when they work on the problem they should pay attention to parallel lines.

Prior knowledge:  The teacher reviews students’ prior knowledge of the school mathematics concept of parallel lines intersected by a transversal.  The teacher reviews different pairs of angles that can be identified when two parallel lines are cut by a transversal.  The teacher tells students, “we have more than what we need today.”  This suggests that the teacher may not want to give away exactly how this prior knowledge will allow students to solve the shadow puppets problem.  By reviewing the relationships from an entire lesson on parallel lines, the teacher is able to remind students of material they should already know, but the teacher does not have to tell students exactly what part of that material they will use to solve the problem.

Other points of interest:  The teacher’s conversation with students follows an IRE/F (initiation-response-evaluation/feedback) pattern where the teacher asks a question, one or more students responds with a short answer, and the teacher provides some sort of feedback to the student’s answer (Mehan, 1979; Wells, 1993).  The teacher’s feedback ranges from very short responses to acknowledge the correctness of an answer (e.g., “yes”) to more elaborated feedback (e.g., “Okay, but you need something more.  Remember you need to talk about your reference.”).  When the teacher asks students to name some of the angle pairs in the diagram, the teacher gives students an opportunity to guide the direction of the discussion, because students can choose what angles to focus on (González & DeJarnette, 2012).  The pattern of interaction between the teacher and students is fairly typical of mathematics classroom interactions.  The extended feedback from the teacher illustrates one way that a teacher can provide extra information to students when performing a review of material before students work on the problem.