To introduce this lesson and help students understand some of NASA's roles in the aeronautics industry, talk about NASA engineers and their work. One challenge for aeronautical engineering is to design planes that can fly long distances while carrying large numbers of people or heavy loads of cargo. Australia and China are two examples of distant destinations where both people and cargo need to go. If the United States can build the best planes to fly to such far-away destinations, we will benefit from increased trade with these countries. Designing airplanes to fly long distances is serious business.
Review the forces that affect flight: lift, weight, thrust, and drag (air resistance). For information about these four forces, see the lesson Rescue Mission Game.
Tell students that they are aeronautical engineers for NASA for the day. Their mission is to design and construct a paper airplane that will travel the greatest distance.
As students make different airplanes to explore the attributes that may affect the distances their airplanes fly, introduce or review the concept of symmetry. Encourage students to observe and analyze their classmates' airplanes.
Pose the following questions your students:
- Which airplanes are similar to yours?
- What attributes do they have in common?
- Which airplanes do you think will travel the same distances as your
airplane? Why?
These same questions can be found on the How Far Can Your Airplane Travel? activity sheet.
After students record their predictions, they should fly their airplanes three times, using the same amount of force each time.
Discuss the effect of the students' force in flying the airplanes. Students should recognize that this is thrust as shown in the diagram above. Discuss the effect of wind resistance as their airplanes fly. Students should recognize that this is drag as shown in the diagram above. Ask students what effect heavier paper might have when flying their airplanes. Students should recognize that this is weight as shown in the diagram above. Ask students how lift affected their airplane "flights."
Students should work with a partner or in a small group to measure their flight distances in inches and record all three distances on a data-collection sheet. To find their median, or middle, distance, students should follow the
directions on the flight data sheet, resource page 16.
Making A Stem-And-Leaf Plot
Have students write their median flight distances on the chalkboard in an orderly, but random way. The following is a sample set of data with the corresponding stem-and-leaf plot.
Sample Data: Median Flight Distances (in inches)
72 74 49 73 92 75 73 82 114 52 82 123 81 67 101
70 76 73 96 73 74 108 57 68 73 41 77 69 112 43
As you record each leaf value in a row of data, cross off the corresponding data point from the original set of data. For example, in the first row of this stem-and-leaf plot, after recording the 1, cross off the 41 in the data set. After recording the 3 in the first row, cross off the 43, and so on.
Continue with this activity until students recognize and describe the pattern for the organization.
Use the following questions to guide the class discussion:
- How are the data grouped or organized?
- What does each row of the graph represent?
- Why do you think that this graph is called a stem-and-leaf plot? What numbers are the stems? The leaves?
- How does this graph help us "see" the data better?
- Do you think that this method is the best way to organize the data? Why or
why not?
After students complete the class stem-and-leaf plot, ask them to line up the airplanes in order from the one that had the least median flight distance to the one with the greatest median distance. Use this display to discuss the range of flight measurements.
If this type of graph is not new to your students, invite them to participate in setting up the stem-and-leaf plot. Ask students what values would be best for the stems. Different responses should be anticipated, depending on their flight results.
Encourage students to use the range of their data to determine what values are needed for the stems. For example, if all distances are 86 inches or more, but less than 240 inches, they may suggest a graph with stems like the sample shown below.
Closing The Activity
Ask students to reflect upon the questions they answered in the activity sheet. Specifically, ask students to refer back to the following question:
Which airplanes do you think will travel the same distances as your
airplane? Why?
Students should compare their hypotheses with the actual results and discuss what factors may have influenced the distances traveled. Were there any airplanes which did travel the same distance as theirs? If so, why?
In addition, this activity can reinforce important place-value concepts. Many students have renamed 21 dimes as 210 cents or $2.10 but have not had opportunities to see that this same type of renaming of numbers can be done in other
applications, such as with units of linear measure. This activity can contribute to students' understanding of patterns and relations among numbers in our decimal number system.
