Chapter 10 Create a Physical Representation Physical representations

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.

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

Palm Jebel Ali, one of the 3 man made islands.

The biggest man made city in the world!

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.

The first completed island.

Students in Math 281 use sand to build models for multivariable functions. The models can help them visualize special characteristics of each function

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

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. It’s okay to have an equal number of each, and it’s 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.

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.

Mexican Restaurant 1. The person who ordered mahi sat next to Ted and across from the person who ordered a burrito. 2. Ken sat diagonally across from the person who ate the fajita and across from the person who ordered beef. 3. The person who ordered a chimichanga sat across from the person who ordered chicken and next to Allyson.

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 Lshape move is completed. No two guards may occupied the same place at any moment, not even just passing. ) Basil Barry Ralph Randy 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)?

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 Lshape move is completed. No two guards may occupied the same place at any moment, not even just passing. ) Basil Barry Ralph Randy 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)?