Overview:  The teacher asks Jonah and Raquel to share two different ways of solving part III the problem.  Jonah had determined the line of symmetry, and he measured the given line segments and tried to create reflections of those segments.  Jonah did not measure any angles, so his drawing is an approximation of the actual design.  Raquel had measured the distances from the given vertices to the line of reflection, and she used those distance to find new points on the opposite side of the line of symmetry.  The teacher formalizes Raquel’s solution with mathematical language and by making notations on the diagram.  The teacher also uses Raquel’s solution to make the perpendicular bisector apparent.  The teacher argues that, because 90-degree angles are easy to make, using the perpendicular bisector is an efficient way to construct reflections.

Prior knowledge:  The teacher in this summary builds from students’ prior knowledge of the school mathematics concept of reflective symmetry.  It seems that students know that pre-images and their reflections are congruent.  To justify the use of the perpendicular bisector in this context, the teacher also acknowledges the mathematical practice of making angles.  By comparing Jonah’s solution with Raquel’s solution, the teacher can highlight that estimating angles can be difficult to do in an accurate way.  Because right angles are much easier to make, the teacher argues that the perpendicular bisector is an efficient way to solve the problem.

Other points of interest:  In this Summary, similar to Summary 1, the teacher uses students’ solutions as a starting point to establish the concept of perpendicular bisector.  After marking Raquel’s diagram, the teacher initiates an IRE (Mehan, 1979) sequence to elicit responses from students about the relationships in the diagram.  It seems that the teacher fishes for responses from students until he elicits the descriptions he has in mind.  With his final comments, the teacher returns to Jonah’s solution and points out to students that Jonah’s solution was not incorrect.  The teacher seems to imply the connection between using the perpendicular bisector and constructing congruent segments, although he does not make these connections explicit.