The Polar Bear Club Question

Date: 17 Mar 1995 17:03:50 -0500
From: Mary Pierick
Subject: Math games

Dear Ask Dr. Math Staff,

I am a fifth grade teacher and I am looking for some 
information on a math game.  I am beginning to think 
this is the ultimate IMPOSSIBLE MISSION!   

Some colleagues of mine remember learning a game called 
Petals Around the Rose (or Petals Around the Rows).  The 
game is played with dice and was designed to help gifted/
talented kids learn what it feels like to hear the same 
directions over and over without understanding them.

If you can find out anything, I would be forever grateful.  
If you can't, maybe you can point me in the right direction.  
I have already tried countless other teachers, math 
professors, and professional journals.

Thanks for anything you can find!

Mary Pierick
Tavelli Elementary
Ft. Collins, CO

Date: 17 Mar 1995 18:31:22 -0500
From: Sarah Seastone
Subject: Re: Math games

Hi there,

One possibility for the game you are trying to find may be a 
riddle that was taught to us at a Geometry Forum workshop 
last summer by Ruth Carver, a math teacher at Mount St. 
Joseph Academy in Flourtown, Pennsylvania.  Unfortunately, 
as an official card-carrying member of the Polar Bear Club, I
am sworn to secrecy and may not reveal the answer.  The 
game does involve dice and directions heard over and over 
without understanding--until the light suddenly dawns.

Here's the riddle, which is printed on the back of the card:

The game is in the name of the game, invented in the days 
of Genghis Kahn, polar bears around an ice hole.  Like petals 
around a rose, you can count each bear's nose.  (Toss a handful 
of dice -- about 6.)  How many polar bears do you see?

Once someone guesses the riddle and can say the right number 
of polar bears for three consecutive tosses of the dice, he or 
she takes an oath not to reveal the secret and becomes a 
Certified Polar Bear.   :-)

I hope this helps.  Very sorry I can't reveal the answer to the 
riddle.

-- Sarah (Keeper of the Dr. Math Archive) Seastone

P.S.  You could write to Ruth Carver directly:
       ruth@mathforum.org --
       I'll send her a copy of this message.

Date: 17 Mar 1995 18:33:34 -0500
From: Anonymous
Subject: Re: math games

Hi Mary,

Now, before I give away the secret, let's try a few rolls:

Suppose the dice came up a five and a four.  Then there 
would be four polar bears.

If it came up a two and a three, there would be two polar 
bears.

If you need more clues, give me a few more rolls to 
respond to with your guess of the number of bears.

-- steve "chief of staff"

Date: 17 Mar 1995 19:18:51 -0500
From: Mary Pierick
Subject: Re: math games

Steve,

Wow, I was looking for something to teach to my 
high-achieving kids and it doesn't sound like you are going 
to make this easy on me!  That's OK.  I think I'm up to the 
challenge.  Nothing scares me--I'm a teacher! :-)

Your clues were intriguing but I'm not sure that I have this 
figured out yet.  I'd very much like to be an official member 
of this club so how about these rolls:

1. roll a one and a two  (answer is zero?)

2. roll a six and a three   (answer is two?)

Go easy on me if my answers are completely crazy.  I have 
heard that higher-level thinkers have more difficulty with 
this game...!

Can you play with more than two dice?  If so, how would 
that  work?  How about some examples?

Thanks for your quick response.  Take your time getting back to 
me this time--I'll be logging off until tomorrow.

Mary Pierick

Date: 18 Mar 1995 09:14:10 -0500
From: Anonymous
Subject: Re: math games

Sorry, I've been sworn to make members earn their membership.  You know how
it is. ; )

"Your clues were intriguing but I'm not sure that I have this figured out
yet.  I'd very much like to be an official member of this club so how
about these rolls:

1. roll a one and a two  (answer is zero?)"

right.

"2. roll a six and a three   (answer is two?)"

right

"Can you play with more than two dice?  If so, how would that work?  How
about some examples?"

Absolutely.  In fact I recommend doing this with five or six dice.

Imagine a roll of six dice.  A six, five, four, three, two, and one come up.

How many polar bears?

-- steve

Date: 18 Mar 1995 14:17:22 -0500
From: Mary Pierick
Subject: Re: math game

Steve,

Your loyalty to the Polar Bear Club is commendable albeit frustrating to 
those of us who are still struggling with the game!  :-)  Rest assured, 
however, that once I am an official member, I will not let someone else's 
frustration sway me from my oath.  In fact, there are a couple of kids in 
my class whose frustration will give me great satisfaction...!

OK, I think I've got it.  If the dice showed 6, 5, 4, 3, 2, 1, I would 
see 6 polar bears.  How'd I do?

Mary

Date: 18 Mar 1995 15:21:02 -0500
From: Stephen Weimar
Subject: Re: math game

"OK, I think I've got it.  If the dice showed 6, 5, 4, 3, 2, 1, I would
see 6 polar bears.  How'd I do?"

Great!  Of course with the kids, I would make it a little harder by giving
them no sample rolls and answers to start with, just the rules.  But we
have to compensate for those of us whose brains are stiff with age.  : )

-- steve