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1999-2000 EPoWs
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Search and Rescue
Shoelaces: 1 | 2 | 3

Customizable EPoWs
Graph Zooming

Search and Rescue
posted May 16, 2000 as a Math Forum EPoW

Introduction: Based on a helicopter flight school theme, this four-page activity addresses mathematical concepts of degrees and angles. Pilots are asked to figure out appropriate headings and distances to reach increasingly challenging destinations.


Where's the Math: The helicopter flight school places students in a "training" role in which they build on their intuitive understanding of direction, distance and angle to encorporate estimation of distances and degrees. In part one, students drag the compass arrow to choose a heading for their chopper, receiving immediate feedback in the change in direction of their helicopter on screen. The compass also indicates the heading they have chosen in degrees. Part two of the problem, the "flight test" allows dragging the compass arrow and to note the corresponding degree heading; however, the helicopter remains at its current heading until students type in the heading and choose to "fly." On their first mission in Part three, students must avoid an obstacle but travel the shortest distance, requiring a two-step solution that may lead to an inquiry into triangular relationships and connections between triangles and circles. Part four requires students to calculate the changes in degree of orientation through positive and negative turns, exploring complementary angles.

Standards: Measurement, geometry

Role of Components: The Search & Rescue problem series uses Geometer's Sketchpad to control the heading via the compass and to animate helicopter movement and based on values from the compass or inputted into number entry fields. Action is 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. String view provides feedback from the flight instructor.

(The applet for this problem is currently unavailable)

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Sample submitted solution:

From:  David, age 13
Jordan, age 13
School:  Issaquah Middle School, Issaquah, Washington

Part IV: License Qualifying Exam

1. A rookie has called in and he needs a flight plan. Here is the map that shows where he is in relationship to the hospital. Use the simulation tools to create a flight plan, and write your plan here. The flight should pass over the way point to avoid the volcano, and follow the shortest possible route.

Leg 1: 4.2 miles, 240 degrees Leg 2: 4 miles, 342 degrees

2. At the way-point, let's say that you want to turn 50 degrees right, but due to engine problems it is safer to turn left. How many degrees left should you turn to make the same change in direction as a 50 degree right turn? Please explain how you figured it out.
310 degrees. We found that if you subtracted 50 from 360 you get 310. We did that because 360 is the amount of degrees in a circle.

Bonus Question:
3. You want to travel to a destination that is at a heading of 200 degrees, but your helicopter is not allowed to fly between the headings of 180 and 270 degrees. Can you still make the trip? Please explain.

Yes, because you could fly past the area you are supposed to go to and turn around and fly back and you wouldnt be in the restricted air space.

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Reflections: It is difficult to comment on how students dealt with the problem due to the fact that we had very few submissions. For the most part, it seems that students could answer question one, but had difficulty on question two understanding how to find the complementary angle using the compass, and with question three in explaining how they got their answer. Students enjoyed interacting with the first 3 pages of the problem. As they interacted with those pages they got an idea of how a compass works and how that relates to flying. The students did not have much trouble answering the first question but when they got to the second question they seemed to think still in terms of the simulation. Because of that they didn't realize that it was a simple question involving thinking about going around the circle in one direction (a certain number of degrees) and going in the opposite direction (three hundred and sixty minus that number of degrees). Once I reminded the students that it didn't necessarily have anything to do with flying the helicopter and that they should just think of a circle, they had an easier time thinking about the problem. The students who had time to think about the bonus question were on the right track but they weren't quite able to express themselves to have it be counted correctly. A great corresponding lesson would be to work on LogoWriter with the turtle turning right or left and the corresponding equivalencies to get the second idea across!

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