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Pirates & Diamonds 1
posted October 1, 1999 as
a Math
Forum EPoW
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Introduction: This problem
challenges students to develop logic
skills and problem-solving strategies
by figuring out sequences of steps
that will allow them to accomplish
tasks not obviously possible with
the tools provided.
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Where's the Math: This problem
draws on students' logical thinking
skills and encourages use of measurement and geometry
concepts.
Standards: Measurement,
algebra,
geometry
Role of Components: The
Pirates & Diamonds series uses
Geometer's
Sketchpad to animate the containers,
which are monitored via number
entry fields (labeled with ESCOT
labels) and triggered by a button
panel. Instructions are displayed
via the HTML
viewer, and solutions are entered
in a
text entry box. Javascript
handles communication among components.
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(The applet for this problem
is currently unavailable)
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Sample submitted
solution:
From: Anna,
age 13
Kai, age 13
School: School of the Arts, San Francisco,
California
The pirate ship has just landed, loaded
with diamonds. You've been sent to buy 8
lbs. of diamonds but you only have one 10-lb.
and one 6-lb. measuring container. How can
you make the purchase?
Fill A and pour it to B. You should
have 6 lbs in the 10 lbs container. Fill
A again and pour again into B. Giving you
a full ten pound container but leaving you
with only two in the six lbs container.
Now empty the 10 lbs container. Pour the
2lbs inside A into B. Giving you 2 lbs in
the 10 lbs container. Now fill A again,
and pour it into B giving you 8 lbs in the
10 lb container.
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Reflections:
There were two basic methods used to solve
the problem. One works by beginning with
container A and the other starts with container
B. Since we hadn't specified that we wanted
a method using the least number of steps,
we counted both methods as correct. Most
students' solutions had only the steps involved
in finding 8 lbs. of diamonds, without including
the amounts that were poured. Since we thought
that the amounts would help people understand
the solution, we only counted it correct
if students included them. Because so many
students left out the amounts, it's possible
that the wording of the problem didn't clearly
ask for what we wanted.
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