Virtual Manipulative
Click here for this interactive resource.
Description
The purpose of this manipulative is to help students recognize that (1) unusual events do happen, and (2) it may take a long time for some of them to happen.
The name "Hamlet Happens" comes from the old idea that if an army of monkeys were to hit the keys of a typewriter (or word processor) randomly, eventually the whole of Shakespeare's play Hamlet would be typed. Of course, the length of time that we would expect to have to wait for such an extremely unlikely event to happen is billions of times the age of the universe.
In this manipulative, letters are drawn at random from the beginning of Hamlet's soliloquy, "To be, or not to be." Any word made from those letters, (such as TOE) of length five or less, can be entered in the box. When Start is pressed, letters are drawn and recorded. The process continues until your word (in the right order) appears (in blue). To facilitate the waiting process, the rate of drawing speeds up as the number of draws increases. Longer words are, of course, less likely to appear, and as the Instructions indicate, "It may take a very long time for words of four or five letters to be randomly produced. You may have to go to lunch or even have a few birthdays."
To help students recognize the randomness of the process, it may be helpful to take a short word like TO and run the manipulative half a dozen times to see that it might take only 4 or 5 draws, or it might just as easily take 50 draws.
As students gain experience and computational skills, this is an excellent setting to try to answer questions such as the expected number of draws to reach a particular word. Words using only letters that appear more than once in the drawing box should be expected to require fewer draws on average than words using letters that appear only once. Then any conclusions reached theoretically should be tested by actually running the manipulative several times to emphasize again that expectations for random processes are just expectations for average behavior and not predictions for any particular run. For example, compare TO and ON; have students see how many draws are required for each word on ten different runs. What was the largest number of draws, the smallest? Compare the average numbers of draws for each word. There should be lots of material for discussion.
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
