Fish Bowl Lesson Plan

This was the original student activity that was created by ESCOT to accompany the Fish Bowl simulation.

1. Introduction: Make a prediction
Suppose now that you are watching a fish swim in a perfectly spherical bowl. Imagine that you could figure out where the fish is at any given time. What percent of the time do you think the fish would be closer to the center of the bowl than to the outside glass surface of the bowl?

1. 12.5% 2. 25%  3. 50%  4. 75% 

The fish would be closer to the center of the spherical bowl (...)% of the time.

2. Run an experiment
One way to check your predictions is to run an experiment. Use the [agentsheets.com/Applets/fish_bowl/ Fish Bowl computer simulation] provided in this activity page to collect data to support your answers.

This simulation is a bit different than the simulations in the previous activities. It has one fish (in the Lonely Fish worksheet) swimming around randomly in a spherical bowl. The simulation keeps track of the position of the fish at all times and knows whether the fish is closer to the center or to the outside glass surface of the bowl. If you look in the lower right corner of the simulation, you will see some "location indicators". You can think of yellow indicators in the same way as points that landed in the inner circle for the activities of the previous weeks.
 * [[Image:In.gif|left]]If the fish is closer to the center of the bowl, the location indicators will be yellow.
 * [[Image:Out.gif|left]]If the fish is closer to the outside the bowl, the location indicators will be red.

To run the simulation for your experiments, follow these steps:

1. Click on the Run button (located under the simulation).

2. While the simulation is running, in the Simulation Properties you will notice that the Total number of position measurements will increase. When it reaches the number you want to sample, stop the simulation and record the results of your experiment. We suggest that you sample 100, 1000, and 10000 position measurements. Unlike the previous activities, for this one you will not enter the number of positions to be generated. The simulation will generate these positions for you automatically as long as it is running.

3. Examine the results to answer the activity questions.

3. Answer Activity Questions
1. According to the simulation, what percentage of the time was the fish swimming closer to the center of the bowl than to the outside glass surface of the bowl?

2. Was your prediction close to the results you got from running the simulation?

3. Write a mathematical explanation that explains the results of the simulation.

BONUS QUESTIONS:

B1. Do you think your answer would change if the fish bowl were larger than the one in our experiment? Why or why not?

B2. Do you think the answer would change if you were running the experiment with multiple fish? Why or why not? You can run the experiment with multiple fish in the bowl using the "Fish Bowl" worksheet. In this case, the indicators are omitted because they won't help you. Instead, watch the simulation properties for the In and Out percentage, representing the probability of the fish being