## "Search and Rescue, Part II" Teacher Support

Search and Rescue, Part II Archived PoW || Student Version

Search and Rescue, Part II is no longer the current ESCOT Problem of the Week. The student version allows teachers to use the problem with their students without giving the students access to the archived answers. Teachers can use the link to the archived problem to get ideas of student thinking.

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Search and Rescue, Part II is a continuation of Part I, which asked students to explore concepts of degrees and angles based on a helicopter flight school theme. In Part II students are applying what they learned in Part I to another situation.

This ESCOT PoW could be used as an exploration of angles, degrees, distance, and headings.

If you have something to share with us as you use any of the links or suggestions on this page (something you tried and changed or a new idea), we would love to hear from you. Please email us.

Alignment to the NCTM Standards - Grades 6-8

Number & Operations
- understand numbers, ways of representing numbers, relationships among numbers, and number systems Geometry
- use visualization, spatial reasoning, and geometric modeling to solve problems

Measurement
- apply appropriate techniques, tools, and formulas to determine measurements

Problem Solving
- solve problems that arise in mathematics and in other contexts

Communication
- communicate mathematical thinking coherently and clearly to peers, teachers, and others
- use the language of mathematics to express mathematical ideas precisely

Connections
- recognize and apply mathematics in contexts outside of mathematics.

Possible Activities:

Pre-Activities

- This ESCOT PoW is related to a very interesting set of mathematics questions on finding optimal boundary lines. Here is one simple example:

Provide students with this question: There are three schools in a town, indicated in the diagram by x, y, and z. You want to draw up town boundaries so that each student is closest to his or her own school. How would you draw the boundaries?

Hints:
Connect point x and point z. Draw the perpendicular bisector of line segment xz. Connect point x and point y and draw the perpendicular bisector of line segment xy. Connect point z and point y and draw the perpendicular bisector of line segment zy. This will give you the solution to your problem.

- Logo activities: since Logo is a computer programming language based on a "turtle" turning right or left and traveling forward or backward, there are a lot of good Logo activities involving heading and distance.

Post-Activities
- GeoPoW: Constructing an Isosceles Triangle - March 24-28, 1997

Suggested by Dennis Sullivan:

The three-school pre-activity suggestion reminded me of a related topic that might provide an interesting post-activity. The intersection of the perpendicular bisectors in the pre-activity problem is equidistant from the three schools. This might make it a good place for a base for the helicopter if the three schools were camps -- if your main criterion is that the flight time from each camp be the same. If you want to minimize the average flight time (and trips to each camp are equally likely) then your goal would be to minimize the total distance from the three points. For this the solution would probably be different. Interestingly, it can be modeled with soap bubbles, which naturally minimize surface area. This type of problem has applications in the placement of high-tension power lines, since minimizing the distance minimizes losses of power due to resistance.

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Resources to use with students:

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