FNR-72 	
1977 
the natural classroom
COOPERATIVE EXTENSION SERVICE, PURDUE UNIVERSITY, WEST LAFAYETTE, INDIANA
Teaching Mathematics in the Forest
by Douglas M. Knudson Extension Forest Recreation Specialist
Many schools have small woods or fields on or near the school grounds. The mathematics teacher, by taking the students into this area, can help them see applications of mathematics principles outside the classroom.
These ideas can be adapted to any kind of math program. High school teachers can augment these suggestions by using algebra, trigonometry and geometry principles in the woods. To begin, you might plan to spend one hour in the fall semester and one hour in the spring semester in the outdoors. The effort will bring rewards, even on a small scale.
You might start by measuring the land and making a big map to scale. As you go through the year, add scaled details to the map, showing locations of measured plots, vegetation, a creek, etc.
■	Find the diameter of a tree. Wrap any kind of measuring tape around the tree at 4 1/2 feet and calculate the diameter (d = C/∏). From this you can determine the area of a circle at 4 1/2 feet (basal area) (A = ∏r2).
■	Then you can calculate basal area of all trees on an acre or hectare. Set up a small 1/5 acre plot (radius of 52.6 feet), or use metric plots. Measure all the trees greater than 5 inches in diameter, at 4 1/2 feet above the ground. Figure the basal area per 1/5 acre plot; multiply by 5 to convert to square feet per acre. (American
foresters find that 80 to 120 square feet of basal area per acre is usually desirable for maximum forest productivity.) Then students can determine how much basal area varies in the woods at various points. They might make recommendations on how managers might improve the condition of the woods, in quantitative terms.
■	Determine distance by pacing. Each student can learn what his step measures in linear distance. This then can be used to do a lot of distance measuring activities. Make sure that the steps are average and are measured over a 100-foot or more course. Compare paces on hills and on the flat.
■	Find the height of a tree. First, guess the height; then check the guesses. There are several methods for measuring or approximating the height:
a.	measure the tree’s shadow, using proportions of the shadow of a measured, vertical stick
b.	determine the angle of elevation and use tangent ratio
c.	use the Boy Scout method of standing a five-foot person beside the tree then stand back and measure the number of five-foot units it takes to get to the top
d.	test precision of the estimates by comparing statistically or graphically
Cooperative Extension Work in Agriculture and Home Economics, State of Indian, Purdue University and U.S. Department of Agriculture Cooperating H.G. Diessline, Director, West Lafayette, Ind. Issued in futherance of the Acts of May 8 and June 30, 1914. It is the policy of the Cooperative Extension Service of Purdue University that all persons shall shave equal opportunity and access to its programs and facilities without regard to race, religion, color, sex, or national origin.