Algebra, Multiplication, and Division of Fractions
and the ER-2


Author: Shannon Dalcerri Wells, teacher credential student, California Polytechnic State University-San Luis Obispo


Audience: Grades 5-7


Mathematical Topics: algebra, multiplication and division of fractions, and measurement


Rationale: According to the NCTM Standards 2000, middle grades students should:

  • become fluent in using symbolic algebra to represent situations and to solve problems (p. 222);

  • be able to solve simple problems involving rates and derived measures(e.g. miles per hour) (p. 233);
  • collect, organize, and represent data (p. 237);

  • apply a variety of techniques, tools, and formulas for determining measurement (p, 232);

  • express mathematical ideas coherently and clearly to peers, teachers, and others (p. 253).

    • In this activity, students will gain experience with measuring time and distance and solving for one unknown. Additionally, students will be given the opportunity to work cooperatively in designing airplanes and they will also have the chance to communicate mathematically by writing essays.

    The NCTM Standards 2000 also emphasize that teachers must help students make legitimate mathematical connections to other areas of study (p. 92) and to use mathematics in applied situations (p. 93). This activity, while giving students practice with multiplication, division, and solving for one unknown variable, also links mathematics to the science of flight.


    Materials:

    picture of the ER-2
    flight and distance table
    directions for making a paper airplane
    one stopwatch per group
    one tape measure per group
    pencils
    8 1/2" X 11 " paper


    Background: NASA Dryden is currently using an aircraft known as the ER-2 to collect information about our atmosphere and environment. The aircraft, based at the NASA Dryden Flight Research Center in Edwards, CA, collects information about our surroundings, including Earth resources, celestial observations, atmospheric chemistry and dynamics, and oceanic processes. By using tools like the ER-2 to intensively study the Earth, NASA hopes to expand human understanding of how natural processes affect people and how people might be affecting them. Such studies will yield improved weather forecasts, tools for managing agriculture and forests, information for fishermen and local planners, and, eventually, the ability to predict how the climate will change in the future. Most notably, NASA Dryden's ER-2's have played an important role in Earth Science research, like studying ozone depletion over Antarctica and the Arctic.

    The ER-2 can fly at high altitudes, as high as 70,000 feet, which is outside of the earth's atmosphere. Depending on the aircraft's weight, the ER-2 reaches a cruise altitude of 65,000 feet within 20 minutes. Typical cruise speed is 410 knots (~690 feet/second). The aircraft can carry equipment weighing over one ton, which is used for sampling, observation, and mapping.

    Learn some facts about the ER-2.
    View several photos of the ER-2.
    View a movie clip of the ER-2.


    The Activity:

  • Begin the lesson by showing a picture of the ER-2. Or, students might use computers to access a variety of pictures located in NASA Dryden's photo gallery. It is important to mention some of the characteristics of the ER-2. For instance, you might want to mention how the plane is used by scientists to gather environmental data about such things as ozone depletion and insect infestations. Learn more about the ER-2 by reading a facts sheet about the ER-2.

  • Describe to students that, in this activity, they will be making paper airplanes and gathering data on the time the plane is spent in the air and its distance traveled. Students will be comparing their data to that of the ER-2 in hopes of better understanding its speed. Also, mention to students how they will be using algebra to compute the speed of their plane, using their time and distance data. Another aspect of this activity is to allow students to work cooperatively to design and test their own aerodynamic plane and then write an essay describing the environmental data they would want to gather.

  • Each student will make a paper airplane. Encourage students to be creative and draw designs on their plane. Also, ask students to write an essay describing the environmental data their plane would collect. Share their essays with the class.

  • Divide the students into groups of 3. Each student will fly his or her plane and record the flight information using the flight and distance table. In each group, students can alternate the roles of pilot (the person who thrusts the airplane into flight), measurer (the person who measures the distance the plane flew), and the time recorder (the person who uses the stopwatch to capture the time the plane spent in flight). Each student should fly his or her plane three times and record the flight and distance for each individual flight on the worksheet.

  • Once the distance and time measurements are recorded, students can now compute the speed of the plane during flight. Prompt students to recall the formula for speed, which is:
    speed = distance / time

    Ask students to first predict the speed, using mental math, and then, using their calculators, students can compute the speed, rounding to the nearest tenth or hundredth. At this point, the teacher should emphasize how the students are using algebra to solve for the variable speed in this equation.

  • After all calculations are complete, students can share their results and determine whose plane flew the fastest and/or the farthest. At this point, promote a discussion by asking students why a particular plane went fastest and/or farthest. How was the plane designed? What other forces contributed to the plane flying fastest and /or farthest? Also, ask students to compare the planes' speeds to that of the ER-2. The ER-2 sure does fly fast!!!

  • Reflecting on those factors that contributed to a plane travelling fastest and farthest, students can now work on groups of 3-4 and, as a team, brainstorm and design an airplane that is "aerodynamically perfect"; that is, flies the fastest and farthest. Using these newly designed planes, students can repeat this activity, collecting flight and distance data. Encourage students to write brief essays describing why they think the design of their plane assisted in reaching its speed and distance traveled.


    • Enrichment Activities:

  • Students might be encouraged to use spreadsheets to create the flight and distance table.

  • Link to this handy unit converter site and allow for students to convert their measurements in feet per sec to miles per hours, among others!



    • Return or go to:

  • Math Activities for Grades K - 4

  • Math Activities for Grades 5 - 8

  • Math Activities for Grades 9 -12

  • Algebra Activities

  • Environmental Research Aircraft and Sensor Technology (ERAST) Program Activities

  • Airborne Sciences Program Activities

  • Math Activities Home Page



    • Funded by the NASA Dryden Flight Research Center


    The below icon appears to help us track statistics on our website.

    Click Here!