Shadow Puppets Launch 6
Overview: The teacher in this launch makes a connection with students’ experiences viewing their own shadows as well as with the historical story of Thales of Miletus using shadows to determine the height of the pyramids of Egypt. The teacher first asks students to think about their own shadows, and students give examples of viewing their shadows while standing outside in the sun. The teacher reminds students that, in the morning or afternoon, students’ shadows were probably not the same length as their bodies. The teacher then transitions to talking about the history of Thales of Miletus, and how he used shadows to measure the heights of the great pyramids of Egypt. The teacher tells students that Thales waited until the time of day when objects were of equal length as their shadows, and then he measured the lengths of the pyramids’ shadows. Students suggest that Thales’s method could be imprecise, and the teacher points out that it may be difficult to measure before the sun moves across the sky. The teacher tells students that through their work on the shadow puppets problem they should be able to devise a strategy that could improve Thales’s method.
Prior knowledge: The teacher first makes a connection with students’ knowledge of the context of the problem, students’ experiences making shadows and seeing how shadows are stretched at different times of the day. Then, the teacher connects with the mathematical practice of measuring an object by comparing it to another thing. Using the example of Thales, the teacher illustrates how one could determine the height of a pyramid by measuring it’s shadow. Thales’s method was not perfect, because it required comparing the pyramid and shadow when they were equal height. The teacher indicates that through their work they should be able to contribute something to increase the level of sophistication of Thales’s practice, hinting that students can relate objects that are similar even when they are not the same size.
Other points of interest: With this launch the teacher introduces a new context separate from the shadow puppets problem with the purpose of establishing a mathematical practice that will translate to students’ work on the shadow puppet problem. Although we do not know from this launch whether students will recognize the connections between the story of Thales and the shadow puppets problem, it seems that the teacher intends to introduce the practice of making comparisons between objects so that students can translate this practice to a new context.