Discussing and Debriefing the Activity As groups report their findings, list their responses in two categories: “What We Know” and “What We Need to Find Out.” Several specific pieces of information should be noted. Point them out if students do not see them. The ceiling is “some thirty or forty feet overhead” (first paragraph), so the pendulum is likely to be about this long. The pendulum is “within three inches of my bosom” (sixth paragraph) when the prisoner develops his plan. The pendulum will take “some ten or twelve vibrations” (seventh paragraph) before it reaches him. “Yet one minute” (near the end of the next-to-last paragraph) is all that is needed until the bandage would be loosened by the rats. A more formal name for swing is period. Introduce this term as the amount of time it takes for a pendulum to make a complete swing (back and forth). This discussion should also bring out that the story might not give students all the information they need (and not all the information in the story is necessarily needed). Explain that, in order to give the initial question some direction and specificity, students must make some assumptions. For example, since they are interested only in the last few swings of the pendulum, they might ignore the fact that the blade is moving down and that the length of the pendulum is changing. Tell students that this unit will use 30 feet as the pendulum’s length (from Poe’s “some thirty or forty feet overhead”) and 12 swings as the duration (from “some ten or twelve vibrations”). However, other assumptions may be needed later. For now, students will explore the following narrower question: How long would it take for Poe’s pendulum to make 12 swings? Post this question on the wall. Students will be working on it, with some digressions, for the rest of the unit. Tell the class that the basic goal of the unit will be to answer this revised question. Ask, What information will you need to answer this new question? How might you get that information? What materials will you need? If students suggest that they could construct a pendulum like Poe’s, tell them that they will eventually do so. However, ask whether they really have enough information at this point to construct a full-scale model of the pendulum. In particular, they don’t yet know which facts about the pendulum are important. You might also bring out that in the real world, actual construction before creating a mathematical model is sometimes too expensive, impractical, or even impossible. Explain that the unit focuses on trying to devise an indirect method to answer the revised question—that is, a method other than building a 30-foot pendulum. The task is to use mathematics to find the answer.