1. Given data on mileage and frequency of trips, students will be able to determine the annual fuel cost for those trips.
2. Students will be able to interpret data related to fuel efficiency from a list of 1994 cars.
3. Students will be able to determine which new cars are the best bargains in terms of fuel efficiency.
4. Students will increase their ability to make informed choices when selecting a new car.
The mathematics portion of this unit revolves around the topic of fuel efficiency in transportation. Throughout the unit, students will gain experience analyzing data. One of the major sources of data will be excerpts from Consumer Reports. In the first activity, students determine the fuel cost of their transportation to and from school for one year. Students will also approximate the lifetime fuel cost for their family vehicle. Given data on all 1994 cars, students will prepare an advertisement for what they believe are the top 5 energy efficient vehicles. They will use the results of their data analysis on fuel efficiency as part of their advertisement.
In the final activity, students need to utilize the April 1994 issue of Consumer Reports. They are asked to choose a new family vehicle. In making their decisions, they will consider size of the vehicle, fuel efficiency ratings, safety factors, reliability, and price.
Prior to the start of the unit, send a Family Vehicle Survey home with each student. This form requests data on the family car (see Appendix B). If some students do not own a family car or do not return the information sheet, ask them to analyze data that you provide for them. This could be fictitious data. Students would probably enjoy analyzing the data from their teacher's driving habits and vehicle.
Rather than jumping right into the first activity, it would be helpful to provide students with some type of rationale for studying fuel efficiency in cars. A visual display illustrating the amount of our state's total energy consumption spent on transportation helps to illustrate the large role which transportation plays in our economy. Transportation in Iowa consumes about 24% of the energy used in our state. (In 1991, electricity accounted for 33% of our state's energy consumption, industry accounted for 24%, the residential sector accounted for 12% and the commercial sector used 8% of the energy consumed in Iowa.) Help students to realize that if each family could decrease their fuel use by even a small amount, tremendous savings would result.
Students will surely wonder how they can go about saving fuel (they don't even have driver's licenses yet). Before you can answer this concern, tell students that they will be taking a look at how short drives each day can really add up to a lot of energy used over the weeks and years. Activity 1 will help to illustrate this point.
Suggestions are provided within each activity for implementing the activities. Possible discussion questions are included.
Teacher Notes
Objective:
Students will determine the fuel cost of driving to and from a particular location in one year.
Materials:
completed Family Vehicle Data Sheet from each student (see Appendix B)
calculators
extra data sets for students who do not bring one from home
Suggested Teaching Strategies:
The purpose of this activity is to illustrate that students can figure out the fuel cost of driving to and from a particular location each day. Furthermore,
when the mileage from these repeated trips is summed across students in one grade, students in one school, students in one county and students throughout the state of Iowa, the amount of fuel consumed is tremendous. Students will
gain experience in manipulating numbers and will be able to make logical conclusions based on the size of those numbers.
Begin the activity by asking students to take a look at how much fuel is used in moving them to and from a particular place each day. Students should choose a place they are driven to and from most frequently. Most students will choose school as the most frequent place they are driven. (You may need to inform students that the school year typically consists of 180 school days.) For those students who ride the school bus or walk, ask them to choose another place they frequently go to on a regular basis. Another alternative would be for students to use the data on their family vehicle survey to determine the amount of fuel consumed by one or both of their parents in going to and from work each day.
For students who do not return their Family Vehicle Surveys and for those who complete the exercise early, have extra data available for students to analyze. For example, ask several key individuals around school to complete one of the Family Vehicle Surveys. Coaches, principals, and other teachers would be good choices. Students may approach the calculations with more enthusiasm if they know that they will be able to explain their findings to those special individuals to whom the data belongs.
Once each student has a completed Family Vehicle Survey to use, present the following problem to the class:
Research Question
What is the cost of paying for the gasoline needed to drive you to and from a particular location for a one year period?
Place students into cooperative groups. Ask each group to make a list of the different information they will need to know to answer the research question. Once student groups have come to a consensus, have each group share their ideas. Based on their ideas, compile a class list. The final list will likely resemble this:
Information Needed to Answer Research Question
total miles traveled per trip
number of trips made in one year (or one school year)
number of miles the vehicle travels on one gallon of gas
cost of one gallon of gas
Let students experiment with performing the calculations. Avoid giving them a formula for the calculations. For those students who are having difficulty, ask them to determine the answer to each of the four points listed under Information Needed to Answer Research Question. This should help steer them in the right direction.
Questions will likely arise as to what to do about the fluctuating cost of gasoline. Some will ask what if the trips were not always taken in the same car? It would be too difficult to consider changing gas prices. Let students know their calculations are approximations. They should make their best guesses about the number of trips and the vehicle used. Their final answers will be useful for comparison purposes.
Answers to Summing Up Questions:
Student answers to all Summing Up questions will vary depending on the particular student data used. Some students may need assistance in calculating their answers to these questions.
Home/Community Connection:
Click here to get the
sample campaign poster
Extensions:
What is the estimated fuel cost for you family car from when you first purchased the car until now? Ask students what assumptions they would need to make to
figure this out. They will need to do some research to discover the average price of gasoline in different years. They will also have to assume the car has been driven about the same number of miles each year, since most people do not
keep records of the number of miles they drive each year.
Student Page
Problem:
Determine the fuel cost of driving to and from a particular location in one year.
Materials:
completed Family Vehicle Data Sheet
calculator
Let's Investigate:
You have probably not given much thought to the amount of fuel that is used getting you to and from school each day. Driving a mile or two doesn't seem
like any big deal. But what if the trip is made every day? What if you consider the number of trips made in one year? What if you consider the number of kids that make that trip each day for one year? The fuel bill may seem to
add up a bit more now. But how much? In this activity you will be getting a better idea of the answer to these questions.
Choose one location to which you are driven to and from at least five days each week. Record the location and the distance from your home to that location.
Use the data from your family vehicle survey to determine the cost of paying for the gasoline needed to drive you to and from your chosen location for a one year period. Work out the answer to this question with your partner. Make a list of the different information you needed to answer this question.
Summing Up:
1. Using data from your Family Vehicle Survey, estimate the total number of gallons of gasoline burned by your family car from the year it was built until today. Be sure to explain how you arrived at your answer. You may also wish to calculate the total cost of this gasoline, based on today's fuel cost.
2. Imagine that your family took along two other kids from your neighborhood on each of your trips. How many gallons of gasoline could be saved by these two extra people not having to be driven in extra vehicles for one year?
3. Imagine that everyone in your class who lives within one mile of school decided to walk to school every day except during the months of December, January, and February. How would you go about figuring out the amount of gasoline that could be saved in one school year by their walking? List all of the information needed to figure this out. If you have enough class data, calculate the answer.
Teacher Notes
Objectives:
Using a list of 1994 cars, students will be able to interpret data related to fuel efficiency.
Materials:
copies of April 1994 issues of Consumer Reports New Car Issue from your library
calculators
Suggested Teaching Strategies:
The intent of this activity is to provide opportunities for students to analyze a relatively large quantity of data. They will then organize portions of that
data in a succinct fashion designed to be understood by and to appeal to the average American.
Divide students into cooperative groups. Assign each group of students the task outlined on the student page. It would be helpful to review the assignment with the class, as a whole, prior to beginning the research process. Ask students to follow the guidelines listed on the student page in making their choices and presenting those choices to the public. Review these guidelines before students begin reviewing their Consumer Reports.
Once students have completed their articles, ask each group to present their finished product to the class.
Sample Answers to Summing Up Questions:
1. Ask students to share their reactions to the different mathematical comparisons used by each group. Which mathematical comparisons did students find best illustrated the fuel economy of the different cars?
2. Fuel cost of 50 miles per gallon car:
$1.20/l gallon x 1 gallon/50 miles x 15,000 miles = $360.00
Fuel cost of 25 miles per gallon car:
$1.20/1 gallon x 1 gallon/25 miles x 15,000 miles = $720.00
Home/Community Connection:
Ask your parents or other family member to name one new car they would like to have. Using the Consumer Reports ratings, show them the data on their
favorite car. Be sure to point out the fuel efficiency for the model. Share your ideas for the five best and worst cars of 1994 with the drivers in your family.
Extensions:
Student Page
Problem:
Interpret data related to fuel efficiency, given a list of 1994 cars.
Materials:
copies of April 1994 Consumer Reports New Car Issue from your library
calculator
Let's Investigate:
In this activity, you will have a chance to analyze a fairly large quantity of fuel efficiency data. You will then be asked to organize portions of your data
in a succinct fashion designed to be understood by and to appeal to the average American. Your challenge is to work as a member of a group taking part in the scenario below. Your group's assignment is given at the end of the scenario.
The Best and Worst of 1994
You are a group of executives from a top newspaper, magazine, or national agency. One of your annual features always presents your agency's pick of the 5 best and 5 worst cars of the year. This year, you are placing a high priority
on fuel efficiency, while giving some weight to safety and several other features. Your findings are always prepared with great secrecy. Your picks are never released early and there have never been any leaks as to what your
picks will be! The article always makes interesting comparisons that help people better understand important numbers by putting them in perspective. Each year, you follow a similar format.
Your job is to choose the Best and the Worst of the 1994 cars. Write an article informing the public of your choices. Be sure to include mathematical comparisons that help people to better understand important numbers by putting them in perspective.
Use the 1994 copy of the Consumer Reports 1994 Car Issue to select your choices for best and worst cars of 1994. Your group should follow these guidelines in making their choices and presenting those choices to the public.
Guidelines
Once your group has completed your rating article, you will be asked to present your finished product to the class.
Summing Up Questions:
1. After hearing each of the different presentations, which mathematical comparisons did you find best illustrated the fuel economy of the different cars?
2. Efforts are being made to greatly increase the fuel efficiency of cars. It is likely that several types of cars will be on the market in the next few years that can travel 50 miles on one gallon of gasoline. Compare the yearly cost of gassing up a car that gets 50 miles per gallon with one that gets only 25 miles per gallon. Assume that the average vehicle is driven 15,000 miles each year.
Teacher Notes
Objectives:
Students will mathematically compare the fuel cost per person for different vehicles and modes of transportation.
Materials:
Consumer Reports 1994 Survey of New Cars
calculators
road atlas of the U.S.
air mileage chart (see Appendix B)
Have an atlas handy in the classroom throughout this activity. Try to find an atlas which contains a mileage table in the back. This would greatly simplify determining the miles for the class trip. Students will also need to know the approximate air mileage from their nearest large airport to their class trip destination. An air mileage chart is contained in Appendix B. You may wish to consult a local travel agent to obtain additional air mileage charts.
Suggested Teaching Strategies:
In the final activity students will compare the fuel cost per person for making a trip to and from a place of their choosing. What makes this activity more
interesting is that students will be choosing their own destination. They will then make determinations of the fuel cost per person for different vehicles and different modes of travel.
You may choose either to distribute the student direction page to each student or to present the activity orally. Directions outlined on the student page should be sufficient to allow you to use either approach.
This activity works best with students working in cooperative groups. Remind students that a consensus must be reached by each group as to the destination of their trip. However, it is not necessary that all groups agree on a location.
Students will need to use an atlas to determine the number of miles by car to their chosen site. Some students may require assistance in using the atlas.
Students cannot ignore the fact that many more passengers can fit into a bus and an airplane than can go in a car or van. It is not really fair to compare planes and buses with family vehicles. Ask students to come up with a way that would be more fair to compare the fuel cost for traveling in each of the vehicles listed. (This can be done by comparing the fuel cost per person, rather than per vehicle. See if students can some up with this idea on their own.)
Make certain that students understand the idea of fuel cost per person. An example might better help them to understand. For example, let's say you are driving a car which gets 25 miles per gallon and holds 5 passengers. If your trip is 500 miles from your school, that would mean the total mileage would be 1,000 miles. Ask students to figure out the gallons of fuel needed for this car to drive the 1,000 miles. (1,000 miles _ 25 miles/gallon = 40 gallons. If the price of gas is $1.10 per gallon, this gas would cost $44.00. If 5 people are in the car, this would come out to $8.80 per person.) Students will need to apply these ideas later on in this activity.
Home/Community Connection:
Do some research to discover the fuel efficiency of one or more of your city or
school vehicles and the total miles traveled each year by the vehicle. This might include police cars, garbage trucks, mail trucks, city maintenance vehicles, school busses, and school vans. Calculate the yearly fuel cost of the vehicle. Can you make any suggestions to your city on how to save money on
fuel? Some students may want to place their data on a spreadsheet.
Extensions:
Challenge students to determine how full the classroom would be if all the fuel was placed in the room for each of these situations:
1. For each student driving alone on the class trip
2. If students carpooled on the class trip
3. For the class trip by bus
4. For the class trip by plane
(Remember, the fuel will need to be totaled since this represents the fuel needed to get your whole class to its destination and back. Students will need to convert their gallons to cubic feet or cubic meters. (1 cubic foot = 7.276 gallons) Students will also need to determine the volume of the classroom and to devise a way of displaying their answers. Sugar cubes, rainbow cubes, unifex cubes or any 1 cm2 cube would work well.
Find out how much fuel is in the underground tanks at a gas station. Discover how often the tank is filled. Based on this figure, estimate the total number of gallons of gasoline sold from this tank in one year. If you live in a small town, your class may be able to estimate the number of gallons of gasoline sold in your town in one year!
Student Page
Problem:
How does the fuel cost per person compare for different vehicles and modes of transportation when going on a class trip?
Materials:
Consumer Reports 1994 Survey of New Cars
calculator
road atlas of the U.S.
air mileage chart
Let's Investigate:
Just imagine....a dream come true! What if you could plan the trip of a lifetime? And to make it even better, what if your entire class could go along! Well, put your imagination to work in this activity because your first task is
to decide on a location. The one catch is that the members of your group must all agree on where to go for the class trip. If you could choose anywhere in the continental United States to go on a class trip, where would you go? Make a list of the locations the members of your group would like to visit.
After discussing your destination as a group, choose one location as the final decision for your trip. What is your destination?
Now, to make matters even better, what if the trip were entirely free, except for one thing...you will each have to pay for the gasoline or other fuel needed to get to and from your chosen location. With this in mind, make a prediction as to which of the vehicles or modes of transportation listed below will take the most fuel per person to travel to the dream spot and back.
Predictions of Fuel Cost per Person
Rate your predictions from 1 (uses the most fuel per person) to 4 (uses the least fuel per person)
a 1994 sports car
a 1994 minivan
a Greyhound bus
a jet passenger plane
Once you have made your predictions, begin working on the Class Trip Challenge presented below. Be sure to complete each of the items outlined in points 1 through 4. Keep organized notes of your calculations for each part of the challenge.
Class Trip Challenge
Destination:
One-way Mileage:
* The estimated fuel efficiency of a 47 passenger bus runs between 5 and 6 miles per gallon, depending on the weight of baggage and whether air conditioning is running.
** The estimated fuel efficiency of a 747 jet which holds 366 passengers, is around 0.139 miles per gallon of jet fuel.
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