Measure Tree Heights With Math

A measuring tape (ideally 50+ feet, or use a known stride length)

A pencil for the pencil method

A protractor, string, and small weight (washer or nut) for a homemade clinometer

A calculator

A notebook and pencil for recording measurements

Choose a tall tree in an open area where you can see the full tree and its shadow. You'll measure its height three different ways and compare.

**Shadow method**: On a sunny day, measure your child's height and their shadow length. Then measure the tree's shadow. The math: (tree shadow / child shadow) x child height = tree height. This is proportional reasoning in action.

**Pencil method**: Stand where you can see the entire tree. Hold a pencil at arm's length. Close one eye. Align the pencil top with the treetop and slide your thumb to align with the tree base. Now rotate the pencil 90 degrees horizontally. Have a friend walk to where the pencil tip now points. Measure the distance from the tree to your friend. That distance equals the tree height.

**Clinometer method**: Make a clinometer by tying a string with a weight to the center of a protractor's straight edge. Stand a known distance from the tree (say, 50 feet). Look along the protractor's straight edge to the treetop. Read the angle where the string hangs. Calculate: tree height = tan(angle) x distance + your eye height.

Compare your three results. They should be close. Discuss why they might differ — shadow angles change, pencil alignment is imprecise, clinometer readings have error margins.

Measure several trees. Rank them tallest to shortest. Estimate age based on species and size.

The shadow method only works on sunny days with clear shadows. The other methods work anytime.

This is real forestry science. Professional foresters use clinometers and laser rangefinders to measure trees. Your child is using the same principles.

The math involved (ratios, proportional reasoning, basic trigonometry) connects directly to school curriculum. This is applied math in the field.

Challenge: can your child estimate a tree's height before measuring? How close is their estimate? Training estimation skills is valuable on its own.