#### Lesson Overview

The story begins with a view of a Cessna 172 Skyhawk (a popular training plane) on the runway -- the student/pilot and a friend have just won free air time, plus \$500 for outstanding work during flight training, and now are preparing for a flight. Before taking off, they must figure out how much fuel is already in the tank, how much more the Cessna can take on, where they might like to fly to, and what it'll cost.

For the group activity, students team up in groups of 3 or 4 to plan trips around their own state, with each team choosing a different point in history (or the future) to plan their trip. Student teams address distances and destinations, time needed, supplies, and places, people and events encountered. Each team can then make a presentation to the class about their own trip.

20-30 minutes

#### NCTM Process Standards

• Standard 1: Mathematics as Problem Solving
• Standard 2: Mathematics as Communication
• Standard 4: Mathematics Connections

#### NCTM Content Standards

• Standard 5: Estimation
• Standard 6: Number Sense and Numeration
• Standard 10: Measurement
• Standard 12: Fractions and Decimals
• Standard 13: Patterns and Relationships

#### Aeronautics Content

• Small airplanes
• Fuel stop planning
• Fuel capacity
• Flight range
• Mileage
• Miles per gallon
• Costs associated with flying
• Destination

#### Objectives

• Students will understand that calculating fuel consumption and flight range is an important aspect of flight planning and flying.
• Students will utilize knowledge of fractions to estimate gallons of fuel and read a fuel gauge.
• Students will calculate the cost of fueling a plane given cost per gallon and number of gallons bought.
• Students will utilize a budget when planning a flight.
• Students will read a chart to determine flight distances.
• Students will plan fuel stops based on the flight range of their craft.
• Students will use estimation strategies to solve problems with money and other decimal units.

#### Prerequisite Skills

• Interpreting graphic representations of fractions
• equivalent fractions
• reducing fractions
• rate problems with miles per gallon and with distance
• multiplying and dividing with one- and two-digit decimals (e.g. money)
• estimation strategies

#### Vocabulary

• flight range - how far your plane can go on a full tank
• fuel capacity - the amount of fuel that the fuel tank holds
• mileage - the number of miles between destinations; also, how many miles per gallon a plane goes; also, the total number of miles a vehicle has gone
• miles per gallon - how many miles a vehicle can go on one gallon of fuel
• destination - the place one is going

#### Materials

Pencil, paper, calculator, MathPad by IntelliTools

#### Class Organization Suggestions

Collaborative groups help with classroom and student management and assist student learning. Optimally, in computer lab settings 2-4 students at one computer support each other and learn effectively. Groups of students can be organized with four students to a computer with each student taking a role: Reader, Navigator, Reporter, Captain.

For example, the Reader reads what is on the screen to the group. The Navigator maneuvers the mouse. The Reporter reports back to class. The Captain keeps track of time and monitors group interaction. Three-student and two-student groups can be assigned a combination of these roles. For instance, Reader and Navigator roles can be assigned to one student while the other student can be the Reporter and Captain.

#### Teacher Tips

PlaneMath provides a means to accommodate students with physical and learning disabilities as well as to enhance math learning for all students. Thoughtful planning and management strategies are effective methods to accomplish these goals. Grouping, functional roles, access to well-designed lessons, learning styles along with student interactions are considerations for management of students. For more information for students with disabilities, contact the Alliance for Technology Access. For additional information, go to the main Teacher's Page for PlaneMath.

1. Have students compare different planes. Which plane consumes the most fuel? the least? Which plane holds the most fuel? the least? Which plane has the farthest range? the shortest range? This would be an excellent graphing activity if each group researched a different plane then added their data to class graphs -- linear graphs of flight ranges, for instance, with 100 miles per inch. Kids could also brainstorm other types of stats for planes as well (e.g. year first built, passenger and weight capacity, runway length needed for take off & for landing, etc.) To find helpful web sites, see below, or do searches for aircraft companies such as Boeing, Cessna, Piper and others. NOTE: for a simpler activity, just compare one or two statistics, e.g. flight range and/or fuel capacity.
2. Divide the class into "flight teams" of 3 or 4 students each. All teams have the same starting point, destination, and budget, but different airplanes. Each team has to plan their flight stopovers, fueling needs and overall budget. Students will write up flight logs and create maps to show how they reached the destination. After presenting, the class can compare stopovers, mileage and expenses, and count the number of ways people chose to go. Students will need to justify their decisions.
4. Visit various aviation web sites (below) to learn how much it costs to train to become a pilot, to buy or rent a plane, etc. Have students graph these costs using units related to other expenses with which they are more familiar (e.g. cost of a car, bicycle, video, candy bar, etc. How many sneakers could you buy for the cost of flight training?)
5. For math practice, have students create a chart of fuel costs, given different gallon amounts and changing prices per gallon. Students can also look for patterns in the chart. See below for helpful fuel price web sites.

We encourage teachers to send us examples of additional problems or activities that they have found useful; we will then post these on this page. E-mail us with your suggestions at planemath@infouse.com.

#### Online Resources

There are many helpful on-line resources listed in our Aeronautics Links page. Some other sites directly applicable to the Fill 'Er Up activity are:

AirNav: Aviation Fuel
Look for fuel in your area, plan a flight with fuel stops, or check on local fuel prices.

SSEC Real Time Data
Geostationary satellite data provided in real time.

Virtual Tourist II World Map
Use this handy site to browse Web sites around the world. Just click on any location on the world map and a list of Web servers in that region of the world (or country) is displayed.

#### Books

Parker, Steve. Inventions in Science: Flying Machines.
New York: Shooting Star Press, 1993.

#### Software

Dreams of Flight: A Comprehensive History of Flight
CD-ROM by Creative Multimedia/Smithsonian)

Imagination Express: Time Trip, USA (CD-ROM by Edmark)