Intent In this activity, students collect data about the periods of pendulums of varying lengths in preparation for predicting the period of a 30-foot pendulum.

Mathematics In earlier investigations, using what they have learned about measurement variation, students narrowed down the possible variables that might affect the time of the swing of a simple pendulum. In this activity, they perform controlled experiments to collect data on the nature of the relationship between the length of a pendulum and its period.

Progression Students work in groups to build pendulums of varying lengths and then conduct experiments to gather data. They compile their results in an In-Out table that the entire class will then use to solve the unit problem in the activity The Thirty-Foot Pendulum.

Approximate Time 25 minutes

Classroom Organization Groups

Doing the Activity Review the status of the class’s progress on the unit problem. This review depends on the class analysis of the amplitude variable in the discussion of Pendulum Variations. However they resolved that issue, explain that today’s experiments will treat length as the only variable. With that in mind, discuss these questions: How will you gather more data on length? What factors will you hold constant so that only the length varies? How will you make sure the data you collect are reliable? As a class, decide on the pendulum lengths to be tested. Remind students that the more points they use and the wider the range of points, the less likely it will be that several different functions could explain their data. Make sure to include both fairly long pendulums, including 6 feet and 8 feet, and fairly short ones, including 1 foot and 0.5 foot. Otherwise the collected data may appear to lie in a straight line. (Students probably shouldn’t test beyond 10 feet or so, because the impact of being able to use the data to make a prediction will be more dramatic if the 30-foot pendulum is significantly beyond students’ earlier results.) With a class of 36 students, you can have each group of four investigate a different length, such as 0.5 foot, 1 foot, 2 feet, 3 feet, 4 feet, 5 feet, 6, feet, 7 feet, and 8 feet. Students may have to tape long pendulums from bookcases or the ceiling. Remind groups that the activity asks them to find the time for 12 periods. Have groups record their data in a single class In-Out table, such as the one shown below, with length as the In and time for 12 periods as the Out. Pendulum length Time for 12 periods

Discussing and Debriefing the Activity When all the data are posted, ask the class, What do you notice about the data? Students are likely to notice that, as the length of the pendulum increases, so does the period. Remind students that their goal is to figure out from the data how long it would take a 30-foot pendulum to make 12 swings. Do you think the relationship between length and period is linear? Someone might suggest graphing the data to find out. You might also mention that after they have completed their analysis (in the activity The Thirty-Foot Prediction), they will test their ideas by actually building a 30-foot pendulum. You may want to spend some time talking about how they might do that, because it will happen soon.

Key Questions How will you gather more data on length? How will you make sure the data you collect are reliable? What factors will you hold constant so that only the length varies? What do you notice about the data? Do you think the relationship between length and period is linear?

Supplemental Activity More Height and Weight (extension) follows up on the supplemental activity Height and Weight by posing the question with a more specific focus. It also incorporates students’ work with curve-fitting.