FNR-72
forestry & natural resources
NATURAL CLASSROOM 
Mathematics in the Forest
by Douglas M. Knudson, Extension Forest Recreation Specialist
•	Estimate the area of a leaf, using the grid method. From that, estimate the leaf area of a whole tree. This will require a number of measurements of various leaves; each participant can have a different size leaf from the same tree.
•	Collect differently shaped leaves on the ground; relate them to geometric figures. Spin-off activities can be developed. For example, by sampling a small area, the number of kinds of leaves can be determined in different months. Then, draw inferences about rates of fall over time and deterioration of leaves on the ground. (Oak leaves generally fall late and stay on the ground longer than others because of their high tannin content. Walnut leaves, however, fall early and deteriorate rapidly.)
•	Saw a log in half. Count the rings; how old is the tree? Notice increases in size of the rings from year to year.
•	How much volume is in a log? Estimate it for short logs using the formula for a cylinder or for entire trees using the cone formula. Across a cut end, determne the volume of wood added in the past one to five years. Measure the width of the ring(s) and of the entire log diameter; determine the volume added as a ratio problem.
•	Find the diameter of a standing tree. Wrap any measuring tape around the tree at 4 1/2 feet above the ground and calculate the diameter (d=C/∏). From this calculation, you can determine the area of the stem or “basal area” (A=∏r2). Use treemeasuring calipers for direct diameter measurement.
•	Calculate the basal area of all trees on an acre or hectare (10,000 square meters). Set up small 1/5-acre plots (radius of 52.6 feet) or use metric plots. Measure all trees greater than 5 inches in diameter
Many parks, forests, and schools have woods or fields where youth groups or classes can learn the practical applications of mathematics. In the woods, the principles of arithmetic, geometry, trigonometry, simple statistics, and many other quantitative skills can be practiced. The abstract nature of the classroom is often a barrier to learning math. In the woods, the individual is counting and measuring tangible things, not black marks on paper. Living skills, not just number exercises, are emphasized.
The following ideas give the leader or teacher a start on developing math exercises. They can be adapted to any age or skill level. For instance, high school teachers can use some of the higher mathematics in explaining the exercises. A leader of young children can concentrate on measuring and counting.
•	Determine distance by pacing. Each young person can learn how long a stride is by stepping off a course and dividing the distance by the number of steps taken. Measure a course over 100 feet long. Compare paces on hills and on the flat. The pace can then be used for distance measuring activities such as estimating the length of a trail, a creek, or forest boundaries.
•	Graphically record the number of occurrences of different phenomena in the woods. For example, how often do trees branch? How many birds are seen on different days? How many different kinds of birds were seen by different people in different parts of the woods? How much rain falls and when? How many different sizes of trees are sampled in an area? Graph them.
•	How many leaves are on a tree? Estimate the number of leaves on several branches, and use ratios to estimate the number of leaves on the whole tree.
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