Run the experiment

  • Click the Test button
  • Enter a positive integer > 0 and click OKAs soon as you see the pattern 4…2…1… appear in the data window, click the STOPALL button
  • Click the Howmany button and the computer will count many “generations” that number took to reach the repeating pattern. The count will appear in the generations window.
  • Think about the results. Record your data and test another number.
  • Repeat

If for some reason an error message is generated by the embedded Lynx project (above), please use this link.

Your challenge

  • Work alone or with teammates to find numbers that take a “long time” to get to the repeating pattern of 4…2…1…
  • How did you go discover a number that took a “long time?”
  • What is a long time?
  • Use any tools at your disposal to learn more about the problem and to record or analyze your data. 
  • Quickly share your hypotheses with the assembled “conference delegates.”
  • Defend your hypotheses.
  • It is the job of the rest of you to disprove the hypotheses of other delegates. Go ahead! Make them look foolish. Mathematics is hardball!

Extra tools to make you say, “hmmm…”
(after a few days of messing about with the original tool)

  • Subsequent pages in the Lynx project above contain additional tools.
  • Click on the Overnight button to ask your virtual lab assistant to keep track of numbers that take more than a specific number of generations. You may adjust the generations slider based on what you determine to be a “long time” and click on the Experiment button to specify the number you wish to start with. This tool will then try every number after the value you specify until you stop it.
  • Clicking on the Graph button will take you to a set of tools designed to graph the number of generations taken by each number in a series beginning with the number you specify. Does the graph tell a story?
  • Change the Logo programs to modify the tools if you’re game.

Next challenge

  • The numbers 54 & 55 take the same number of generations (110) to get to 4…2…1… What can this pair of adjacent numbers possibly have in common to create this phenomena?
  • Are there three adjacent numbers that take the same long time? Four? Five? Does it have anything to do with place value?

Debriefing questions

  • What did you learn from this experience?
  • What did you observe about the learning style(s) of your collaborators?
  • Which subject(s) does this project address?
  • What might a student learn from this project?
  • For age/grade is this project best suited?
  • What would a student have to know before successfully engaging in this project?

© 2003 – 2023 Gary Stager