Intent

Students reexamine the excerpt from the short story “The Pit and the Pendulum,” this time with more specific questions in mind.

Mathematics

The pendulum in the story is 30 feet long, and the prisoner estimates that it will swing 12 times from when he develops a plan of escape until he can carry out the plan. The goal in this activity is for students to state the mathematical question that will frame the unit: Does the prisoner have time to execute his plan? What does one have to know about this situation to predict how long these 12 swings will take?

Progression

Students revisit the excerpt to search for information they can use to answer the question of whether the story’s hero really has time to carry out his escape plan. A class discussion will then help them to restate the question in more quantitative terms.

Approximate Time

25 minutes

Classroom Organization

Groups, followed by whole-class discussion

Doing the activity

Before students reexamine the excerpt in their groups, it may be helpful to have them generate a list of “things we know” and “things we need to know” to focus their thinking on the question of whether the prisoner can escape.

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.

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.

Key Questions

What do we know from the story?

What do we need to know to decide whether the prisoner can escape?

What information and materials do you need to answer the unit question?