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Topic: Day 5 Math Forum Advanced Summer Institute
Replies: 0

 Sarah Seastone Posts: 1,240 Registered: 12/3/04
Day 5 Math Forum Advanced Summer Institute
Posted: Jul 12, 1998 1:08 PM

In response to participant interest, the final full day of the 1998
Math Forum Advanced Summer Institute was re-dedicated to project work
and participant activities. After some initial time for project
development in the Dupont lab, the group moved across the hall for two
presentations:

Rob Rumppe posed this question:

"A student has to be able to weigh any object in integrals from 1 gram
to 255. If each weight costs \$1, what is the least he'll need to pay?"

While several people soon arrived at an answer of \$8 by directly
listing combinations and then extrapolating to find a pattern, Rob
showed another solution and that the answer to some problems may not
be as interesting as _why_ that solution answers the problem, stating
the first few cases of the optimal solution and then motivating and
arriving at a binary representation of integers, a method that
appealed to many participants. A fuller exposition of Rob's activity
is on the Web: see Weights and Binary Digits:

http://forum.swarthmore.edu/workshops/sum98/rumppe.activity.html

Marjorie Ader then distributed handouts she uses as an introductory
activity in her Algebra III class, where she emphasizes groupwork and
brainstorming multiple strategies to answer this problem:

"A camel is sitting by a stack of 3000 bananas at the edge of a
1000-mile-wide desert. He is going to travel across the desert,
carrying as many bananas as he can to the other side. He can carry up
to 1000 bananas at any given time, but he eats one banana every mile.
What is the maximum number of bananas the camel can get across the
desert?"

After some trial and error, groups independently began to refine
strategies for solving this classic problem, also found in the Ask Dr.
Math FAQ at

http://forum.swarthmore.edu/dr.math/faq/faq.camel.html

Marjorie gave some hints, suggesting an incremental approach and
pointing out that 1) the camel does not have to go all the way across
the desert in one trip, but can cache bananas along the route; 2) the
answer contains a fraction; and 3) the camel need not be thought of as
traveling one mile, then eating one banana, but rather as continuously
eating bananas at the rate of one per mile. Soon participants became
so involved in sensitivity analysis or considering extensions of the
problem by varying the parameters that the activity ran well past the
time alloted for it.

Desert:

After lunch and some more work on participant projects, John Goebel
showed how Mathcad can be used to do and share real math on the
Internet. He sends his distance learning students Mathcad files, which
they are able to modify and save, and they then do labs on Mathcad and
e-mail John their papers. Current versions of Mathcad allow you to
embed links to other files or URLs, making them very interactive.

John also shared some of the capabilities of Adobe Acrobat Writer for
putting math on the Web, as live linkable documents and as
high-quality printable documents. For more about his activity, see
Mathcad: Doing and sharing real math on the Internet:

http://forum.swarthmore.edu/workshops/sum98/goebel.activity.html

Finally, June Dershewitz, Chris Alexander, and Judy Ann Brown of the
Forum staff held a break-out session for those interested in their
Puzzler software, currently under development, to be used to
administer the Problems of the Week (POWs) offered by the Math Forum:

Elementary Problem of the Week
http://forum.swarthmore.edu/elempow/

Middle School Problem of the Week
http://forum.swarthmore.edu/midpow/

Geometry Problem of the Week
http://forum.swarthmore.edu/geopow/

For dinner participants visited an Ethiopian restaurant in West
Philadelphia, returning later to the lab for a last session on their
Web projects.

- Richard Tchen and Sarah Seastone, The Math Forum