This resource addresses a practical environmental problem of the number of trees that need to be cut down to supply all the paper the school uses in one year. Students use their knowledge of similar triangles, Pythagoras’ theorem and algebra to design and construct a Biltmore stick used to measure the diameter and height of a tree. They measure some trees, calculate their volume and use the density of the tree to find the dry mass of the tree. They estimate the amount of paper used in the school and, hence, estimate the number of trees that need to be cut down to supply the school’s paper needs.

This sequence follows the reSolve Year 8 resources Circumference and Area of a Circle. The sequence uses similar triangles and the formula for the volume of a cylinder. Significant algebraic skills are assumed when students are asked to work out the diameter markings on a Biltmore stick or they may use the d-tape from Lesson 3 of the Circumference sequence.

### Lesson 1: A Biltmore Stick

Students make a Biltmore stick that measures both the diameter and height of a tree, using knowledge of similar triangles, Pythagoras’ theorem and some challenging algebra.

### Lesson 2: How Many Trees?

Students use a d-tape (see reSolve Year 8 Circumference) or a Biltmore stick to measure the diameter and height of a tree. They use known wood densities to calculate the biomass of a tree and, hence, estimate the number of trees needed to provide the paper that is used by their school in one year.

Last updated June 21 2020.