# Overview

## Using Bicycles to Measure Distance

Developed by Paul Hartzer, Fall 2011
Topic: Geometry
Purpose: This was developed as a field trip lesson plan. I have not had to opportunity yet to teach it.

# Objectives and Materials

## Objectives

Discuss different ways of solving the same problem, in this case, measuring long distances.
Explore the use of wheels to measure distance.
Hypothesize about how measurements change as wheel diameters change.
Measure a given section of sidewalk by riding a bike.
This unit can optionally be combined with a trigonometric lesson involving measuring by relative height.

## HCSEs

G1.6.1: Solve a multi-step problem involving circumferences
L2.1.6: Recognizing when exact answers aren’t possible or practical

## Resources and Materials Needed

For each group of 4-5 students:
A flexible measuring tape
A yardstick
A wheel (wheels should be of different sizes and structure)
A bicycle with properly inflated tires
Playing cards or some similar material
Writing implements, paper, and calculators

# Lesson

## Introduction and Lesson

In the classroom, begin by discussing how students might calculate long distances. Ask students to estimate various distances, perhaps of objects visible outside, or distances to home, and so on, and to justify their answers. (Possible ways to measure: By measuring perceived height of known objects at a distance, by counting off paces, by counting wheel rotations, [for longer distances] by comparing lightning to thunder.)
Ask if any students know how speedometers and odometers work. Guide discussion on wheel/axle rotations. Introduce wheel materials.
In groups of four to five, have students examine their wheels. Ask them about the relationship between the size of the wheels and their circumferences. Each group should measure two wheels. First, measure the diameter (or radius) using the ruler/yardstick and then calculate the circumference using πd. Next, measure the circumference using the measuring tape to verify the calculation. This second measurement reinforces the formula, but be prepared to discuss why the measurements may not be exact.
Reconvene at a public park or other venue (if not already there) with bicycles, one per group. Identify a landmark along the sidewalk at a distance. Have each group measure the diameters of at least one of their wheels, then insert a playing card in the spokes for the purpose of counting rotations (test materials of choice on a bicycle prior to class to make sure they’ll fit securely and make an audible noise).
Each group then approximates the distance to the landmark by riding or pushing their bikes and counting rotations.

## Practice and Closure

Guided Practice: Show how to measure the diameter, and how to calculate circumferences. Demonstrate technique by measuring the length of one wall of the classroom.
Independent Practice: Measuring as groups, counting clicks and calculating distances.
Afterwards, have each group share their approximated distance. Discuss why there might be variation in the results: Tire inflation, not a perfectly straight line, bumps in the sidewalk, incomplete rotation. Presumably, most approximations will be close to each other; proximity of results can be used to assess understanding.
Discuss that this method can be reversed to calculate how many times a bicyclist pedals based on going a known distance.