Intent Students immerse themselves in the unit problem by building their own pendulums, trying to time one full swing, and then reporting their results to the class.

Mathematics The period of a pendulum is the time it takes for the bob of a pendulum to swing from some point P along its entire path and back to P. The most convenient point P is the point of maximum displacement from the vertical. In this activity, students will devise their own techniques to try to measure a pendulum’s period.

Progression After a quick orientation, students will work on the activity at home and bring in their results to share with the class.

Approximate Time 5 minutes for introduction 25 minutes for activity (at home) 15 minutes for discussion

Classroom Organization Individuals, followed by whole-class discussion

Doing the Activity Have students brainstorm how to build a pendulum from materials found at home. It need not be elaborate, but as students will want to be somewhat accurate in measuring the period, talk about items they should consider using and not using.

Discussing and Debriefing the Activity Have students share their pendulums and what they have discovered in their groups, and then ask a few groups to report their findings to the class. Some students may have timed several swings and then divided by the number of swings; others may have measured several individual swings and averaged the results. There is no single best way to measure the period of a pendulum; there are pros and cons to each method. For example, it is easier to make a single measurement of the time required for several swings than it is to do several measurements of one swing at a time. On the other hand, a student could argue that timing several swings in one measurement is not a valid method because the pendulum gradually slows down. If students do not have different approaches, there is no need to pursue this issue now; its importance will be examined in What’s My Stride?

Key Questions How did you measure the period of your pendulum? What problems did you have in measuring the period?

Supplemental Activity Getting in Synch (extension) presents the concept of period in a different context, through which students will explore some number theory. The activity can be assigned at any time, as the term period is introduced in the first activity. For whole-number periods, the questions are fairly straightforward, but for fractions, the issues get more interesting. Question 3 hints at an idea that Greek mathematicians called incommensurate numbers. This refers to a pair of numbers that we would today describe as having a ratio that is an irrational number. Don’t expect students to get the correct answer to this question. [Link to math maps]