Speedometer and Odometer Accuracy

The activities in this Pull-Out focus on developing a model to describe the effect of changing the size of a vehicle's tires on the accuracy of its odometer and speedometer. In Activity 1 students determine tire diameter from tire-size labeling; for example, 265/75R16. This involves finding a percentage of the tire's width (given in millimeters), then converting the result to inches. After working through this activity, students should be able to set up a direct variation between actual mileage and odometer mileage; the coefficient of variation depends on the current tire size compared to the size of the factory-installed tires. For homework, students apply what they have learned to the problem of speedometer accuracy. Up to this point, students work through a new set of calculations each time a new tire size is given. Their major task in Activity 2 is to create an Excel spreadsheet "conversion calculator" that calculates tire diameter from the tire size, actual mileage from odometer mileage, and actual speed from speedometer speed. The three change-in-tire-size scenarios presented in Activity 2 were taken from questions posted online by vehicle owners.

Mathematics Prerequisites and Discussion:

Students should have some experience converting measures of length from one unit to another. If not, introduce this topic before students begin working on this Pull-Out. If students are unfamiliar with spreadsheets, show them how to set up a control panel and enter simple formulas. (See Lesson Notes for Activity 2.)

Mathematics Prerequisites and Discussion:

Calculators, access to Excel (or another spreadsheet) for Activity 2.