Math Activity
with Forester's Tools

Students discussed what tree measurements (age, circumference, and height) are needed in order to calculate the amount of timber that can be collected from a tree. Students were introduced to the forester's tools (clinometer, Loggers' tape and diameter tape measures, and increment borer) that make the job faster. Then, students conducted field investigations in in which the tools were used to take the appropriate measurements.

  • Age of trees: The age of the trees is determined by taking a core sample from the tree and counting the rings. Students realized very quickly that there were 2 methods for calculating the age: count all the rings and divide by 2, or count only the dark rings.
  • Diameter and circumference: The diameter and circumference of the trees are calculated using 2 special measuring tapes. A diameter tape is calibrated in increments of pi which converts the measurement from circumference to diameter for the forester.

    A logger's tape is calibrated in increments of inches and feet and is used for measuring distance from a tree. (The other side is often calibrated in increments of pi so that the logger's tape can serve as a regular measure and a diameter tape).
  • Angles to measure height: Height is measured using a clinometer. The clinometer uses trigonometry to calculate the height by determining the angle opposite the tree. The forester stands 100 feet from the base of the tree (a distance measured using the logger's tape). Then, the clinometer reads the angle between the forester's eye and the top of the tree. At 100 feet, the angle measurement is the same as the height of the tree (plus the height of the forester!)
  • Estimation: The number of board feet is estimated using a forester's chart that converts the height of the tree and the circumference of the tree into board feet.


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