Create a Physical Representation

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Chapter 10 Create a Physical Representation
Physical representations fall under the major
problem-solving theme of Spatial Orientation. A
physical representation lets you look at the
problem in many perspectives and even let you
touch the problem, not just represent it by a
picture.
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Example 1 Developers often hire model builders
to make architectural models for their future
constructions in order to attract clients.
Palm island project in Dubai, United Arab Emirates
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Palm Jebel Ali, one of the 3 man made islands.
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The biggest man made city in the world!
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The World will consist of 250 to 300 smaller
private artificial islands divided into four
categories private homes, estate homes, dream
resorts, and community islands. The cost of an
estate island ranges from 15 millions to 45
millions.
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The first completed island.
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Students in Math 281 use sand to build models for
multivariable functions. The models can help them
visualize special characteristics of each function
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Letter Cube The three drawings below are
different views of the same cube, which has a
letter on each of its six faces. Draw those
letters on an actual cube to determine the
positions and orientations of the letters.
T
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Jackals and Coyotes Three jackals and three
coyotes are on a trek across the Mokalani Plateau
when they come to a river filled with carnivorous
fish. There is a rowboat in sight, and the party
decides to use it. (Both species are known for
their cleverness.) However, the boat is too small
for any more than 2 of the group at a time. So
they must traverse the river in successive
crossings.
There is one hitch, though The jackals must not
out number the coyotes at any time, in any place.
For example, if two jackals and only one coyote
are together on the western side of the river,
this problem is reduced to simple subtraction
the jackals will kill,
and eat the coyote. Its okay to have an equal
number of each, and its also okay to have more
coyotes than jackals. So, the trick here is to
use the one small rowboat, a lot of sweat, and a
bit of brainpower to ensure the coyotes safety
while both group cross the river.
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Mexican Restaurant Four friends (one named
Janie) went out to dinner at a Mexican
restaurant. The hostess seated them in a booth.
Each ordered a different meat (pork, mahi-mahi,
beef, or chicken), and each ordered a different
kind of Mexican dish (tostada, burrito, fjita, or
chimichanga). Use the clues on the next page to
determine which person ordered which dish and the
kind of meat that it contained.
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• Mexican Restaurant
• The person who ordered mahimahi sat next to Ted
  and across from the person who ordered a
  burrito.
• Ken sat diagonally across from the person who ate
  the fajita and across from the person who ordered
  beef.
• The person who ordered a chimichanga sat across
  from the person who ordered chicken and next to
  Allyson.

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Worchestershire Palace At Worchestershire
Palace, four guards are pacing back and forth
performing maneuvers. Two of the guards are
wearing blue uniforms (Basil and Barry) and the
other two guards are wearing red uniforms (Ralph
and Randy). They are performing their maneuvers
for an audience. The guards are standing in
large tile squares on the floor. The tile
arrangement with each guard's present location is
shown below.(Each move is an L-shape move and no
one else can move until an L-shape move is
completed. No two guards may occupied the same
place at any moment, not even just passing.)
Barry
Basil
How many of these moves does it take for the blue
guards (Basil and Barry) to change places with
the red guards (Ralph and Randy)?
Randy
Ralph
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Worchestershire Palace At Worchestershire
Palace, four guards are pacing back and forth
performing maneuvers. Two of the guards are
wearing blue uniforms (Basil and Barry) and the
other two guards are wearing red uniforms (Ralph
and Randy). They are performing their maneuvers
for an audience. The guards are standing in
large tile squares on the floor. The tile
arrangement with each guard's present location is
shown below.(Each move is an L-shape move and no
one else can move until an L-shape move is
completed. No two guards may occupied the same
place at any moment, not even just passing.)
Barry
Basil
How many of these moves does it take for the blue
guards (Basil and Barry) to change places with
the red guards (Ralph and Randy)?
Randy
Ralph