Center for Technology and Teacher Education: Mathematics Activities

(1) Place a state map on the center of your work area. Place a compass on the map centered at your current location. Orient the map so that North on the map is in the direction of North on the compass.

The tasks in this activity are designed for the map of Charlottesville, VA (click here for view of map). When conducting the lesson in your classroom, it may be beneficial to adapt the tasks to correlate with maps of your specific location.

(2) Give directions from Charlottesville to Lynchburg ‘as the crow flies.’ Be sure to include a bearing and a distance in your directions. Explain your directions.

(3) Determine the city that is approximately 18 miles from Charlottesville along a bearing of 275 degrees. What would be the bearing from this city back to Charlottesville?

(4) The bearing N10⁰W is equivalent to the bearing 350 degrees. Explain this equivalence.

(5) Determine the city that is approximately 24 miles from Charlottesville along a bearing of N47⁰E. What would be the bearing from this city back to Charlottesville?

(6) Suppose a passenger jet flew 17 miles due east of Charlottesville, and then flew 25 miles due north before being forced to make a crash landing. The rescue squad called for the medi-vac helicopter known as ‘Pegasus,’ which is located at the University of Virginia Hospital in Charlottesville. What bearing and distance should Pegasus fly to go directly to the crash site?

(7) Point your web browser to ExploreMath’s “Points in Polar Coordinates” Activity located at:

(8) Notice how the units (i.e., q) on the graph are labeled. Compare this to the labeling of degree measurements in part 1. Predict the location on the graph of a point with coordinates (4, 135⁰). Drag the orange point from the bin to the location you predicted and note the coordinates of the placement. Now adjust the coordinates of the point so the point is located exactly at (4, 135⁰).

Exact placement of points is difficult. For more accurate placements, type the desired coordinates of the points to the right of the slide bars. You must press enter after typing in values.

(9) Drag the blue point onto the plane, such that the blue point has coordinates (4, q) 135⁰. Determine two values (one positive and one negative) for q q 135⁰, so that the blue point and the orange point will coincide on the graph. Check your answers by typing in the appropriate values to the right of the blue sliders.

Note: When two points coincide on this activity, only the last point placed will be visible.

Note: Definitions of r vary. For this activity, r is defined as directed vector, not a radius. Thus r can take on negative values. The user may want to adjust this activity to match their preferred definition of r.

(10) Drag the purple point onto the plane, such that the purple point has coordinates (r, 315⁰). Determine a value for r so that the purple point will coincide with the other two points on the graph. Check your answer by typing in the appropriate values to the right of the purple sliders.

(11) Using the information from tasks 9 and 10, construct expressions that will generate the coordinates of all points that coincide with the point located at (r, q).

Answer: (r, q)= (r, q+ n*360⁰) = (-r, q+ (2n – 1)*(180⁰)), for n = 1, 2, 3…

12) Look at the figure below. Given r and for point P, determine general equations for both x and y in terms of q. Now suppose an that x and y are known. How could r and q be determined?

Use the fact that tan q = (opposite)/(adjacent). Also, remember that tan^-1 q is only defined in quadrants 1 and 4.

Treasure Hunt is a game in which teams of students use compasses and 100 foot (or meter) tapes to navigate around a large field. The object of the game is to be the first team to reach the treasure chest.

Click here for a sample layout of the Treasure Hunt Game.

Each team is assigned a starting location. At each starting location there is a card with an angle and bearing on it that leads to the next ‘way point.’ At each way point there is a treasure (e.g., Hershey kisses) and a new very small card with directions to the next card. Teams navigate their way through the course collecting cards and treasure. The final card for each team leads them to a common ‘treasure chest.’ The first team to arrive at the treasure chest with all their cards is declared the winner.