Overview:  At the conclusion of the lesson the teacher recalls the example of Thales of Miletus using shadows to measure the heights of the pyramids of Egypt.  The teacher asks students to compare and contrast the shadow puppet problem with Thales’s problem of measuring the pyramids, and students note some of the differences.  The teacher reminds students that Thales waited to measure the length of the pyramid’s shadow until midday, when the shadow was equal to the height of the pyramid.  But the students in the class, using similar triangles, could set up proportions to find lengths when the shadow was not the same size as the puppet.  The teacher uses this as an opportunity to remind students that there is a proportional relationship between an object and its shadow, both in the case of the shadow puppets and in the case of the pyramids.  The teacher relates students’ work on the problem to Thales’s problem by saying that Thales could have used their strategy of identifying similar triangles and solving a proportion to find the height of the pyramids.

Prior knowledge:  The teacher recalls students’ prior knowledge of the mathematical practice of measuring shadows.  This summary seems to follow Launch 6, because it seems that the teacher and students have already discusses Thales and the measuring of the pyramids in class.  Thales established a mathematical practice by comparing the height of an object to the length of its shadow to determine the object’s height.  The teacher points out that by employing knowledge of school mathematics, specifically the concept of similar triangles, students could improve the sophistication of Thales’s method.

Other points of interest:  With this summary (and presumably the launch that would have preceded it) the teacher translated between different contexts to establish the common practice of measuring shadows.  This provides a contrast to Summary 1, in which the teacher compared different mathematical solutions within the single context of the shadow puppet problem.