Teaching about Bearings

Date: 06/08/2000 at 05:56:24
From: Amy Vyse Widdicombe
Subject: Bearings

We have to teach a math lesson for one hour about bearings, and we 
don't have a clue as to what bearings are. We have to locate a point 
using two bearings. Also, can you think of any activities to entertain 
the class instead of making it a boring lesson? We want it to be fun.

Help us; we don't know what to do.

Date: 06/08/2000 at 13:04:02
From: Doctor Rick
Subject: Re: Bearings

Hi, Amy.

First of all, a bearing is a compass direction. That is, it's the 
angle between north and the line between two objects. The bearing from 
where you are (point P) to some object (point A) is the angle between 
a line going north from point P, and the line from point P to point A.

If you're in geometry class, then the ability to locate a point P 
using bearings to two points A and B is a consequence of the 
angle-side-angle congruence theorem. The bearings aren't the same as 
the angles of the triangle, but if you know the bearing from point A 
to point B, as well as the bearings from point P to points A and B, 
you can find all the angles of the triangle ABP. You'll want to expand 
on these concepts.

So much for the blackboard explanation. There's lots of room for 
making this fun, and no excuse for a boring lesson! The best way would 
be to hold the class outdoors and have some games in which you look 
for "buried treasure" where the clues are the bearings from two trees 
to the treasure. You'll need to get hold of at least one magnetic 
compass. By the way, you can make up the clues by standing at the 
"treasure" and taking bearings to the two trees. How are these 
bearings related to the bearings from the trees to the treasure? You 
must be sure you know which way the bearings go.

If you have to be in class, you could have a student leave the room 
or be blindfolded, then choose another student to take bearings from 
his/her seat to two corners of the room. Then the first student comes 
in or takes the blindfold off, and tries to determine which student 
you chose, using the bearings the chosen student measured.

You'll want to give some training in using a compass before you do any 
games. If you have to be indoors, some odd things might happen if 
there is a lot of metal in the room.

Here are some Web sites I've found that may give you some ideas:

   Conning and Pilotage - John Jacq
   (how to find where you are in a boat)
   http://www.axs.com.au/~jjjacq/sundry/navconn.html   

   Map and Compass - Search and Rescue Society of British Columbia
   http://www.sarbc.org/m&c.html   

   Measuring Distances-Triangulation - Explorer lesson plan
   http://explorer.scrtec.org/explorer/explorer-db/html/783751625-447DED81.html   

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/