TITLE: Triangulate in the Wild

SUBJECT: Geometry

TOPIC: Construction of a Triangle

INTERACTIVITY:

The student will choose a card from Envelope 1. On the card will be an angular measure. There were an equal number of 15°, 25°, 30°, 40°, and 50°.cards in this board's Envelope 1.

The student will lay out the string provided along the direction of the measure on the chosen card using the paper protractor located on the bottom left section of the board.

The student will choose a card from Envelope 2. Like the cards in Envelope 1, each in Envelope 2 will also have angular measure written on it. There were an equal number of 20°, 35°, and 50° cards in this board's Envelope 2.

The student will lay out the string provided along the direction of the measure on the chosen card using the paper protractor located on the bottom right section of the board.

The student will find that the strings intersect at a point and will record the number on the tree which they find located at this point of intersection.

DIRECTIONS FOR USE: I posted these 3 direction sheets along the bottom center of the board.

You are a wildlife biologist. You want to find Tina, a black bear. She has a radio transmitter attached to her and you can measure her signal using your receiver and antenna.

She has known you since she was a cub and allows you near enough so that you can follow her and record her natural behavior for hours. But, first, you must determine her general location so that you can cover most of the distance over roads in your jeep before having to set out on foot.

The trees represent large sections of forest, and, with two measurements, you can determine her approximate location.

- Go to Location 1 on the left and take a card from Envelope 1.
- The number on the card is the angle your antenna was facing when you measured the strongest signal.
- Notice the string at Location 1. It will act as your straightedge.
- Make sure that one end of the string is pinned in the hole at Location 1 and extend the string so that it is straight, pinning the other end in the forest or beyond so that the string crosses the angle on the card.
- Go to Location 2 on the right and take a card from Envelope 2.
- Repeat Steps 2-4 at Location 2.

- The strings should intersect and the point of intersection is where we might expect to find Tina.
- Take a Worksheet from the folder below and record the number on the tree that's nearest your point of intersection.
- Retain the two angle cards. You will submit them with your completed Worksheet.
- The remaining activity on the Worksheet can be performed while at your desk or at home.

TIME: A student will need 10-15 minutes to complete this activity.

SPECIAL CONSTRUCTION: The background, border, lettering, and graphics were all constructed using posterboard. The background, border, directions, and protractors were stapled in place. The letter and graphics were glued. I used the images below to create the board's protractors and two grizzly bears. Like the letters, the trees were created using the templates in the library's AV Center, but creating the bears required intermediate-level scissoring.

CREDIT: The students will receive a homework grade for completing the activity. It will account for 1 of 10 homework grades in the 9-week quarter.

OTHER COMMENTS: Initially, I planned just to have trees randomly arranged and ask the student to identify the tree nearest the point of intersection. But during construction, I decided that the arrangement should be more precise so that each point of intersection very close to the center of exactly one tree. I knew that I'd need to restrict the angular measures available in the envelopes so that each pair of measures would result in a point of intersection. The most obvious case being I could not have a 90° card in both envelopes. But, later, I recognized that an exactly precise arrangement would mean that I must further restrict the angular measures on the two sets of cards so that a tree lie at the intersection of each combination of measures. The table below shows the 15 possible combinations so the answer trees were not symmetrically arranged.