# The Wave

Introduction

Introduce this experiment by organizing students into one large circle and then having them demonstrate the "sports stadium wave (People stand up with their hands in the air and then sit back down.) Alternatively, have the students stand side by side with their arms to the left. Have the students create a wave by sweeping their hands over their heads from left to right, each person starting as the one before finishes.

In this experiment, the duration of a wave is approximated by a linear function of the number of students participating in the wave. This is a whole-class experiment involving three steps: collection of data, finding the equation, and interpreting the data

Materials

Stop watch or clock with a second hand

Graph paper, one sheet per student

Procedure

1. Start with a group of five students. To do the wave, the first student stands up with his/her arms above his/her head, and sits down.
2. The second student does the same. The last student says "stop" as he/she sits down.
3. The timer has the responsibility of saying "start" at the beginning, and of recording the elapsed time when the last person says "stop".
4. Repeat this experiment with 8, 10, 15, and 18 students. Different numbers of students can be used — it’s fun to go around the whole classroom once or twice.

Questions:

1. Record the data from this experiment.

Data Collection
Independent
(number of people)
Dependent
(time taken)

2. List the ordered pairs to be graphed. Graph these points on a coordinate plane.

3. State the rule (equation) for the relationship between the number of people (x) and the time taken (y) for the wave in the experiment.
1. Two points on the graph:
2. Slope:
3. Equation:

1. How long would it take for 100 students to do a wave?
2. How many students are necessary for a 30-second wave?
3. Was your answer in b) a whole number? Does a non-whole number make sense?

5. What if …?
1. How would your graph be different if every student stood up and turned around twice before sitting down? Explain.
2. How would your graph be different if the first person wasn’t paying attention and missed the "start", not beginning the wave for 5 seconds? 