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Search
and Rescue Paths
Posted January
14, 2001 as a Math Forum EPoW
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Introduction: In this problem,
students fly a helicopter to different
locations by specifying headings
and distances.
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Where’s the Math: This
problem introduces the concept of
vectors in an interactive way. By
specifying a distance and a direction
(instead of an angle from the origin,
an angle relative to true north),
a vector corresponding to the helicopter’s
movement is specified. By becoming
familiar with the behavior of vectors
in the simulation, students can
investigate adding vectors by realizing
that, in one movement, they can
end up in the same spot as with
two other, different movements.
The relationship between the distances
and angles of added vectors, as
well as other vector properties,
can also be experimented with in
this simulation.
Standards: Measurement,
geometry
Role of Components: Geometer's
Sketchpad was used to create
the simulation, and a custom bean
runs the simulation. A custom bean
allows specification of distance
and direction. A button
panel is used to start and/or
reset the simulation. String
view displays messages regarding
the simulation.
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Try
the first applet!
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Try
the second applet!
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Sample submitted solution:
From: Alex, age 14
School: McLean High School, McLean,
Virginia
1. After reading the question above,
and using the map under question 1 with
three camps, write your flight plan here.
To cut down on mileage, I chose the shortest
route to each destination. Here is a chart
showing the starting point leading to the
destination, and the heading and distance:
Paths (Heading, Distance)
1. Base to the Green Camp (230 degrees,
2 miles)
2. Green Camp to Base (45 degrees, 2 miles)
3. Base to the Blue Camp (90 degrees, 4
miles)
4. Blue Camp to the Red Camp (315 degrees,
4 miles)
5. Red Camp to Base (180 degrees, 4 miles)
2. There are a number of possible flight
plans to accomplish your task. Describe
how one way could be better than others.
The flight plan I chose is better than another
plan because the path that I plotted is
the shortest route to all of the destinations.
The route I take uses the least mileage.
You can reach all of the destinations in
a 16 mile round trip. By cutting down on
the mileage you cut down on the time taken
to make the trip which can be important
if there are injured individuals onboard.
The faster you get back, the better, and
my route is better for that reason.
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Reflections:
In this puzzle, students were given applets
to practice with, and then asked to apply
what they had learned to a map that wasn't
interactive. That was different than most
of the puzzles we've seen. I like this use
of applets, but I think a lot of students
didn't expect it, and maybe didn't read
carefully enough to see what they were supposed
to do.
I visited a lab in which some middle school
students were using this ESCOT Problem of
the Week. (Thanks for having me, Wilmington
Friends School!) It looked as if most kids
had fun with the applets and with figuring
out the solution to the problem. I also
noticed that some of the computers couldn't
handle opening two applets one after the
other -- it crashed the machine. We're going
to have to pay more attention to memory
issues. The other thing I saw was that some
people were confused about how to get the
second simulation to go with the three legs
of the trip if they only entered one leg
at a time. They just weren't quite sure
how to go about it. It turns out that it's
possible to test the route one leg at time,
or enter all three at once.
Looking at all the solutions submitted,
here were the areas that seemed confusing
to many students:
Some people got confused with the compass
directions; a heading of 0 is always north,
no matter where you start. Some people wrote
north, south, east, and west instead of
the compass headings. Some people used the
second applet for their flight plan instead
of the map under the question. Oops! Some
people counted a diagonal in the map as
one mile when it's actually a little more
than that (a side of a square in the map
is equal to one mile). And some people simply
forgot to make a stop back at the camp.
All in all, some good work was submitted in response to this problem.
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