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.
How should the winner of The Biggest Loser be chosen? Students compare pounds lost vs. percent lost, and analyze historical data to determine which method produces the fairest game.
Topic:
Quantities (Q), Ratios and Proportional Relationships (RP), Statistics and Probability (SP)
Why do concert tickets cost so much? Students use percents to describe how much of a ticket’s price goes to various parties -- artist, venue, brokers, etc. -- and debate the fairest ways to price and sell event tickets.
How does life expectancy affect how you live your life? Students use proportions to determine what life expectancy must have been in the past in order for the phrase "30 is the new 20" to be accurate, and explore how life might change as life expectancy changes.
How much should you pay for a shared wireless plan? Students use proportional reasoning to predict whether a family will go over their minutes, messages, or megabytes, and decide how much each person should pay.
Topic:
Expressions and Equations (EE), Number System (NS), Ratios and Proportional Relationships (RP)
Who should buy health insurance? Students use percents and expected value to explore the mathematics of health insurance from a variety of perspectives.
Topic:
Number System (NS), Ratios and Proportional Relationships (RP), Statistics and Probability (SP)
How do aspect ratios affect what you see on TV? Students use ratios to explore why the image doesn't always fit on the screen, and examine how letterboxing might affect their favorite movies.
Topic:
Geometry (G), Ratios and Proportional Relationships (RP)
How much should vowels cost on Wheel of Fortune? Students use ratios and percents to explore what would happen if Wheel of Fortune charged prices for vowels based on how often they come up.
Topic:
Ratios and Proportional Relationships (RP), Statistics and Probability (SP)
How dangerous is texting and driving? Students use proportional reasoning to determine how far a car travels in the time it takes to text. Students discuss the dangers of distracted driving and generate strategies for helping drivers and passengers stay safe.
How accurate are police speed guns? Students use rates and the Pythagorean Theorem to examine the accuracy of LiDAR guns used to catch speeding drivers.
Topic:
Expressions and Equations (EE), Geometry (G), Ratios and Proportional Relationships (RP)
Are coupons always a good deal? Students reason with percents and proportions to evaluate enticing coupons and debate whether retailers should be allowed to raise the price of items in order to then put them on sale.
Topic:
Expressions and Equations (EE), Ratios and Proportional Relationships (RP)
Why do tires appear to spin backwards in some car commercials? Students apply unit rates and the formula for the circumference of a circle to determine what makes a spinning wheel sometimes look like it’s moving in the opposite direction of the car sitting on top of it.
Topic:
Geometry (G), Ratios and Proportional Relationships (RP)
Should people with small feet pay less for shoes? Students use unit rates to calculate how much different-sized shoes cost per ounce and debate the fairest way for manufacturers to charge for their shoes.
How should students be graded? Students use percent change to evaluate how changes to a grading policy would affect students and discuss the fairest way to balance mastery with effort.
Topic:
Ratios and Proportional Relationships (RP)
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Mathalicious lessons provide teachers with an opportunity to teach standards-based math through real-world topics that students care about.
How have video game consoles changed over time? Students create exponential models to predict the speed of video game processors over time, compare their predictions to observed speeds, and consider the consequences as digital simulations become increasingly lifelike.
Topic:
Building Functions (BF), Interpreting Categorical and Quantitative Data (ID), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE), Seeing Structure in Expressions (SSE)