Need for Speed : A Lesson by Mathalicious

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Everyone knows that speeding is dangerous. We have speed limits for a reason: speeding drivers are more likely to get into accidents. But in addition to bodily harm, what about the damage speeding can do to your wallet?

In this lesson, students learn that beyond a certain speed, a car’s fuel economy (the distance it can travel per gallon of gas) decreases the faster it goes. They use unit rates to compare the time saved when driving fast to the additional fuel cost, and interpret graphs to explore how fuel economy varies with vehicle type. Taking into account all of these factors, they then discuss what they think the highway speed limit ought to be.

Students will

Use unit rates to calculate how long it would take to drive a certain distance and what the fuel cost would be
Interpret graphs to understand how fuel economy varies with the type of vehicle
Discuss the implications of different speed limits on fuel economy

Before you begin

Students should be familiar with unit rates and how they are calculated (e.g. if a car travels 481 miles on 13 gallons of gas, it travels 481÷13 = 37 miles per gallon). One question requires some graph interpretation, so it will help if students have had some exposure to graphing in Quadrant I.