Simulated Experimental Coin-Toss Data submitted by: Jeff LeMieux, June 2003 This narrative describes how I use my javascript tool, cataloged in the Math Tools digital library, in the classroom. Course: Math 7 Topic: Probability, Experimental Probability Resource type: JavaScript Resource location: http://www2.whidbey.net/ohmsmath/webwork/javascript/cointoss.htm Math Forum catalogue entry: http://mathforum.org/mathtools/tool.html?rc=tool&new_id=790 Story:  Most lessons on probability start with a coin toss. Students can quickly see that there are really only two practicable results - heads and tails. However, students also bring a fair amount of experience to the lesson. They have flipped coins and either been 'lucky" or "unlucky,' often without giving much thought to the fairness of the exercise. One way to demonstrate the idea of probability is to conduct experiments. In this case, flip a coin 10, or 20, or maybe even 100 times and keep a tally of the results. If each student or pair of students in the class does this there will be a pool of data to compare the experimental probability with the theoretical probability. Unfortunately, the typical sample of data obtained in a classroom setting is relatively small. Students will tire of flipping and recording coin tosses, but they remain curious about the possibilities of doing large numbers of coin tosses. This script allows students to investigate large numbers of trials using a simulation for tossing the coins. While the limits as to how many "coins" can be tossed in one event depend on processor speed and available memory, repeated trials of 1000 and 5000 are certainly feasible. One cautionary note. Kids really do enjoy seeing the big numbers of heads and tails appear and will quickly attempt to 'max out' the machine. It serves as a good introduction to the large numbers of trials needed to accurately determine experimental probability. Where and how I used this: I use this script after the introductory lesson and lab where students do in fact flip their coins and record the results. Usually we tally the class results and then compare them with several trials of the script based on their the classes total tosses, e.g. if 15 pairs of students completed 50 tosses each that would represent a total of 750 tosses for the class. We would then run the script with 750 trials and compare the results. This would probably be repeated several times with the results noted. This script will also come in handy later when the question of tossing multiple coins once (i.e., 3 coins) versus 1 coin three times, etc. Send comments to Jeff LeMieux at tackweed@whidbey.net Jeff LeMieux, June 2003 http://www2.whidbey.net/ohmsmath