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Course, Subject

Algebra II (Next Generation), Math, Science & Technology, Mathematics (NYS P-12 Next Generation)

Virtual Manipulative

Click here for this interactive resource.

Description

This virtual manipulative uses a random number generator to model tossing a coin repeatedly and records the results.

For beginning students, the actual experience of tossing a coin is undoubtedly worth­while. With a whole class tossing a coin, it is fairly easy to collect data on more than a hundred tosses and the results of several hundred-tosses experiments can be tabulated. It should become apparent rather quickly that while we expect about half the tosses to come up heads and half tails, that exact distribution doesn't happen very often. With this Coin Tossing mathlet, students can explore such questions easily and quickly.

Questions of probability are easily explored. How often should we expect to get four tails when we toss a coin four times? If we toss a coin ten times, how likely is it that we will get four heads in a row? With this mathlet, we simply set 4 as the number we want for the Longest run of heads and watch the results. The machine tosses the coins and records the results, continuing until there is a string of four heads. We shouldn't be surprised that different trials come up with different numbers. For example, we got four heads in a row first with 4 tosses, then with 18 tosses (twice) and then with 30 tosses. Moving from simple observations and recording to doing some computational work to answer the question theoretically is a natural progression.

With a little imagination and experience, this simple tool is versatile enough to model a remarkable variety of statistical experiments. The suggestions on the Instructions page are just a beginning.

Content Provider

The National Library of Virtual Manipulatives is a three-year NSF supported project to develop a library of uniquely interactive, web-based virtual manipulatives or concept tutorials, mostly in the form of Java applets, for mathematics instruction (K-8 emphasis). The project includes dissemination and extensive internal and external evaluation. For more information, please visit http://nlvm.usu.edu/en/nav/vlibrary.html.

Credits

Principal Investigators
Larry Cannon
Jim Dorward
Bob Heal
Leo Edwards

Java Applet Programming
Ethy Cannon
Joel Duffin
David Stowell
Zeke Susman
Richard Wellman
Jennifer Youngberg

Web Site Programming
Joel Duffin

Related Academic Standards

New York State

NY-7.SP.8 Find probabilities of compound events using organized lists, sample space tables, tree diagrams, and simulation.

NY-7.SP.8a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

NY-7.SP.8b Represent sample spaces for compound events using methods such as organized lists, sample space tables, and tree diagrams. For an event described in everyday language, identify the outcomes in the sample space which compose the event.

NY-7.SP.8c Design and use a simulation to generate frequencies for compound events.

AII.S.CP.4 Interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and calculate conditional probabilities.

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