Re: Challenge Question #2 rebuttal

From: "Verl L. Smith" <>
Subject: Re: Challenge Question #2 rebuttal
Date: Sun, 10 Nov 96 16:53 EST

Hi Chris & all,

I presented the answer to Challenge #2 to my physics class because the
concept of not being able to see the other side of the canyon bothered me:

"...if you stood on one rim of the Valles Marineris, you wouldn't be able to 
see the other rim because it would be out of sight over the horizon !"

I asked my class:
"How can the other rim of a chasm be "over the horizon" -- what is rising out
of that chasm to block the view?  Or - how shallow is this canyon that its
floor becomes the horizon?  Maybe I need a picture (or profile to scale) to 
help visualize this."

Philip grabbed the challenge and came up with a very good response.  Basically
for the far wall of the canyon to be over the horizon (the horizon being the
floor of the canyon itself) the canyon must be 200km or more in width and be
1.5km or less in depth.  According to the data we dug up on Marineris, the
maximum width is about 200km, but the depth is up to 7 or 8km.

Philip first did use calculus to solve the problem, but the solution he
presented here relies only on geometry & a little trig.  I would hope that
the readers of this list would be able to follow his presentation with 
careful reading and maybe digging some long unused math concepts out of some
corner of our brains.

Philip is truely a gifted student and a joy to work with - even though he
often operates at a level beyond me.  We explore and learn together; I cannot
say I teach him, he often teaches me.

As for the level of the questions - Chris asked:
>More fuel for the fire, says I.  We need challenge questions we can
>attempt to SOLVE.  How can my 5th graders and I be expected to generate
>these kinds of responses???  Surely we are not expected to generate that
>level of response!  

I am new to this list, but from what I have observed by looking at the 
student responses posted all levels are accepted.  The challenge questions
are answerable at different levels.  Obviously 5th graders wouldn't be 
expected to answer the way Philip did, but they should be able to think
through the questions and provide their own answer - even if it misses the
mark.  The emphasis should be on getting the students to think at their level
and reason through to an answer.

I say on to Challenge 3 - have you tackled that with your class?  Get three
volunteers up in front of your class and have them do a Martian moon dance
and play with rotating & revolving to grasp the concept.  It should be fun.

Verl Smith
Ava High School
Ava, MO