tag:blogger.com,1999:blog-78554979842894787.post269678582114805807..comments2013-09-26T23:28:10.838-07:00Comments on Wyoming Math Teacher Circle: Tootsie Roll Game (“Iterated Sharing” from Solve This)gdlhttp://www.blogger.com/profile/03316706312218120708noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-78554979842894787.post-9327533493972641192012-05-26T08:23:02.008-07:002012-05-26T08:23:02.008-07:00Yes, this is an awesome activity to engage kids bu...Yes, this is an awesome activity to engage kids but as said in the article it proven to be hard with my class of 16 students. But I used the given idea in the article to split my class in two groups. Both groups made their own <a href="http://www.areacircle.com" rel="nofollow">circle</a> and perform the activity.<br /><br />It turned to be an awesome, fun and educating activity for kids.Manjithttps://www.blogger.com/profile/09161629919203395902noreply@blogger.comtag:blogger.com,1999:blog-78554979842894787.post-8366875265494402562009-12-07T14:57:05.145-08:002009-12-07T14:57:05.145-08:00I've been returning to this problem in convers...I've been returning to this problem in conversations over and over. I have a student who promised to make a C++ interactive game of it ... and I'll let you all know if that happens.<br /><br />I also wanted to note that the problem as stated in Tanton's book says that we only pass HALF our candies to the left, keeping half, and playing with the same rule that if anyone ends with an odd number of candies, one draws an extra from the (inexhaustible) pile of extras.<br /><br />A little extra play has revealed that in a circle of 10 people where the holding of one player is increased by 2 and the end-state is investigated, there seems to be a critical value beyond with the play --- using Ariane's rules --- becomes oscillatory. At lower levels the limiting value obtained is related to the numbers involved in the oscillating set of values.Lynnehttps://www.blogger.com/profile/02298838629222120903noreply@blogger.comtag:blogger.com,1999:blog-78554979842894787.post-70752431194264068672009-11-09T15:19:12.484-08:002009-11-09T15:19:12.484-08:00This comment has been removed by the author.Lynnehttps://www.blogger.com/profile/02298838629222120903noreply@blogger.comtag:blogger.com,1999:blog-78554979842894787.post-3100066443618012562009-11-09T14:28:52.198-08:002009-11-09T14:28:52.198-08:00This was a wonderful activity, the kind that you c...This was a wonderful activity, the kind that you could throw at anyone. I used it during advising week:-)<br /><br />My own investigations focussed on a circle of three people, and I looked at the case where one person had more than the others. I wanted to know how the final shared amount was related to the starting amounts in this case. No results yet, except to say that (1) the longest run so far is 11 rounds; (2) the shortest run is 2 rounds; and (3) two adjacent evens have the same end game, e.g. whether the 3rd person has 22 or 24 extra, or 46 or 48 extra, the endgame is all having 10 extra or 18 extra, respectively.<br /><br />Ariane also noted that she got the problem from James Tanton's book "Solve This: Math activities for students and clubs." This is the second problem in the book, and a solution to the initial challenge is in the back. They don't attempt to describe the pattern of how the game ends. Instead, they argue that in each round the maximum # anyone holds doesn't exceed the max of the first round. Those holding fewer candies experience growth in their share unless surrounded by people with the same numbers. Since we can't have unsustained growth of integers in a bounded interval, we must admit that all eventually have the same amount.<br />is bounded above and that the lower bound is always rising.Lynnehttps://www.blogger.com/profile/02298838629222120903noreply@blogger.com