Lesson Plan

# Hybrid Cars versus Gas Cars

Students will use systems of linear equations to identify whether it is worth (monetarily) to pay extra, upfront, for a hybrid car as opposed to a fully gasoline powered car.
Steven M.
Classroom teacher
Gateway Middle School
Monroeville, United States
My Subjects Math
Objectives

Objectives:

1. Students will be able to determine the cost effectiveness of buying a hybrid versus a traditional gasoline car.
2. Students will analyze linear equations to determine when the additional cost of purchasing a hybrid will equal the cost of a traditional gasoline car.

PA Core Standards:

• A1.1.2.1.3: Interpret solutions to problems in the context of the problem situation (linear equations only).
• A1.1.2.2.1: Write and/or solve a system of linear equations (including problem situations) using graphing, substitution and/or elimination (limit systems to 2 linear equations).
• A1.1.2.2.2: Interpret solutions to problems in the context of the problem situation (systems of 2 linear equations only).

Citation: (This lesson is adapted from the following site)

Subjects
Math
Science

#### 1 Hook

Free, Free to try, Paid

#### Class opening question(s): (Discuss these questions with your students)

• Many care owners are concerned about the gas milleage of their car. Over the past 10 years, the cost of gasoline has increased by about 100%! (In 2008, the average price of regular gas in the U.S. was about \$4.12, about a 135% increase since 2004)

Have the students journal about these questions or conduct a class discussion.

Use Poll Everywhere to conduct a poll of whether students think it is worth it to own a hybrid.

Use Padlet to have students respond to the questions below:

1. What advantages are hybrid cars to the owner?
2. What are possible disadvantages for the owner?

#### Comparing a 2013 Honda Civic LX vs. 2013 Honda Civic Hybrid.

 Car Cost Difference in Cost City Miles/Gal Highway Miles/Gal Average Miles/Gal Cost of Gas for 1 year (12,000 miles) Honda Civic Sedan \$18,318 ( -----) 28 39 34 \$1291 Honda Civic Sedan Hybrid \$23,406 \$23,406 - \$18,318 = \$5088 44 44 44 \$1000

The current cost of gasoline can be found at http://fuelgaugereport.opisnet.com/PAmetro.asp.  Make sure you choose the Pittsburgh Area to have an accurate price and record the price of a regular gasoline.

What is the cost of gasoline in the Pittsburgh area?

Compute the cost of gas for one year using 12,000 miles per year, the cars gas mileage, and the average cost of gasoline for the Pittsburgh area. (See information in last column in the chart above)

#### Creating a System of Equations

Car Total Cost = (Difference in Cost) + (Cost of Gas for 1 year)x

That will give us the following equations:

Honda Civic Sedan Total Cost = 0 + 1291x

Honda Civic Sedan Hybrid Total Cost = 5088 + 1000x

#### Graphing the Equations

Using the Desmos site, graph the equations found above allow x equal the number of years of ownership and y equal the cost of the car.

#### Solving the Equations--Graphically or Algebraically:

Solve the equations using the website or algebraically

Click on the link to view the graph:

https://www.dropbox.com/s/h7pf8gpl6t80csb/Screenshot%202014-10-08%2010.15.34.png?dl=0

Algebraic method

1291x = 1000x + 5088

1291x - 1000x = 5088

291x = 5088

x = 5088/291

y is about \$22,592.50 of costs

#### Readdress the opening questions: (Depending on class time you may want to end day 1 at this point)

1. Is the hybrid worth it?
2. Is it worth keeping the car for 17.5 years

Free, Paid

#### (Possibly the beginning of day 2)

The informaton be created in Google Docs or even a Google Form.  This will allow you to to "collect" the information from the students.  Demos has the option of sharing a chart via Google Drive.

Now it’s your turn! (Students can work with a partner or groups of four)

1. Now, you will research the cost of one more vehicle and its hybrid counterpart.
2. What is the cost of gasoline/gallon?  __________________________________

Complete the table below:

 Car Cost Difference in Cost City Miles/Gal Highway Miles/Gal Average Miles/Gal Cost of Gas for 1 year (12,000 miles)

Have the students answer these questions either during class or for homework

1. Where did you find this information? _____________________________________ (website)
2. Write a linear equation for the total cost of each car.
3. Graph the linear equations that you found comparing your cars using the graph paper below.
4. Determine the point of intersection and describe its meaning in the context of the problem.
5. Using the same equations, solve them algebraically, using any method of your choice.