Using Rates to Determine Efficiency

Using Rates to Determine Efficiency

Denzel and Jason Discuss Cars

Opening

Denzel and Jason Discuss Cars

Watch the video.

  • What information does the video tell you about the situation?

Math Mission

Opening

Express the fuel efficiency of a car as a rate.

Find Fuel Efficiency

Work Time

Find Fuel Efficiency

Denzel and Jason took different approaches to solving the fuel efficiency problem. Look at each approach and then answer the following questions. Remember to specify the appropriate unit, such as miles per gallon or gallons per mile.

  • What is the unit rate in Denzel’s calculation?
  • What is the unit rate in Jason’s calculation?
  • Who calculated the fuel efficiency correctly?
  • How far could Jason’s dad travel using 16 gallons of gas?
  • Jason’s dad drove the car 150 miles. How much gas did the car use?
  • Which rate—Denzel’s or Jason’s—was most helpful in answering each question?

Hint:

  • What are the quantities involved in the problem?
  • What operation do you need to use in order to find the rate?
  • In the last lesson, to find the unit price you divided the total price by a quantity. To determine the fuel efficiency of a car, should you divide miles by gallons or gallons by miles?

Prepare a Presentation

Work Time

Prepare a Presentation

Summarize Denzel’s and Jason’s thinking about fuel efficiency. Use your work to support your summary.

 

Challenge Problem

Miles per gallon and gallons per mile are called inverse rates.

  • Does dollars per pound have an inverse rate? If so, what is it?
  • Write several rates and their inverse rates. Why do you think one form of the rate is usually used?

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about your classmates’ thinking with regard to expressing rates for gallons and miles.

Hint:

As your classmates present, ask questions such as:

  • What are the quantities in this situation?
  • What operation did you use to find the unit rate? Explain your thinking.
  • Does your answer make sense? Explain.
  • When would you use Denzel’s way of expressing the rate?
  • When would you use Jason’s way of expressing the rate?

Comparing Fuel Efficiency

Work Time

Comparing Fuel Efficiency

Denzel’s mom’s car can travel 450 miles using 20 gallons of gas. You know that the fuel efficiency of Jason’s dad’s car is about 20 miles per gallon.

  • Which car is more fuel efficient? Defend your answer.

Hint:

  • What are the quantities in the problem?
  • How can you express the fuel efficiency of Denzel’s mom’s car in miles per gallon?
  • How can you compare the two rates?

Motorcycle Fuel Efficiency

Work Time

Motorcycle Fuel Efficiency

Jason’s brother has a motorcycle.

The motorcycle can travel 210 miles using 3.5 gallons of gas.

  • Do you think its fuel efficiency will be more or less than that of Jason’s dad’s car? Explain your thinking.
  • Express the fuel efficiency rate in miles per gallon.
  • Express the fuel efficiency rate in gallons per mile.

Hint:

  • What are the two quantities in the problem?
  • If you want to find the rate miles per gallon (mpg), or miles divided by gallons, what quantity must be in the numerator?
  • If you want to find the rate gallons per mile (gpm), or gallons divided by miles, what quantity must be in the numerator?

Characteristics of Rate

Formative Assessment

Summary of the Math: Characteristics of Rate

Read and Discuss

  • Fuel efficiency can be described using two rates: miles per gallon and gallons per mile. More miles per gallon means greater fuel efficiency; but fewer gallons per mile also means greater fuel efficiency.
  • Fuel efficiency in miles per gallon (mpg) is a rate. You will find mpg useful for finding how far you can go on any number of gallons of gas.
  • Fuel efficiency in gallons per mile (gpm) is also a rate. You will find gpm useful for finding how many gallons of gas you need to go any number of miles.
  • The smaller the rate in gpm, the greater the fuel efficiency.
  • The rates 20 mpg and 0.05 gpm describe the same situation. They both describe the relationship between 300 miles and 15 gallons.

Hint:

Can you do the following?

  • Explain what miles per gallon andgallons per mile mean.
  • Include the term rate .
  • Discuss how to define the fuel efficiency of a car.

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

Something new I learned today about rates is …