## Long Distance Airplanes

• Lesson
3-5
2

Students make paper airplanes and explore attributes related to increasing flight distances. Each student collects data from three flights of the airplane and finds the median distance. Students then collect, organize, display, and interpret the median distances for the class in a stem-and-leaf plot.

This lesson was adapted from Travel in the Solar System in Mission Mathematics II: Grades 3‑5, a NASA/NCTM project, NCTM 1997.

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.

Assessment Options

1. This activity provides a variety of assessment opportunities. In their discussions, encourage students to:
• Share their conclusions with the class;
• Summarize the class activities: they made predictions, flew airplanes three times, determined median distances, displayed data in a stem-and-leaf plot, used the graph to draw conclusions about their experiment and data, and recorded their conclusions;
• Identify the median, mode, and range of their class data set;
• Explain what each row of numbers in the class stem-and-leaf plot represents.
2. As students use the stem-and-leaf plots, check that students' plots contain all data points in the correct rows and have an appropriate title. As the activity ends, check that students make and record appropriate concluding remarks about the class activity and data.

Extensions

1. Students can decorate and identify their airplanes with their initials and flight distances. Share the following aviation information with them. All airplanes have a letter and number combination painted on their surfaces for identification purposes. Each set of letters and numbers is registered and belongs to that airplane only. The letter and numbers are called in by the pilot to identify the airplane to airport control towers and base operators when requesting airport information for landing. Other aircraft in the vicinity are also able to hear the call and be aware of the airplane's presence. The identification letters are called in by using the phonetic alphabet. Give students a copy of this alphabet. The numbers are called in one at a time, with only one change. "Nine" is pronounced "niner." Students can turn their papers 90 degrees counterclockwise so their stem-and-leaf plots are facing sideways. Ask these questions: What do you notice about our graph when we turn our display sideways? Does it remind you of any other type of graph with which you have worked before? What similarities do you notice between the stem-and-leaf plot and the bar graph? What differences? Does holding you stem-and-leaf plot sideways help you see the results more easily? Explain.
2. While students have their stem-and-leaf plots turned 90 degrees, have them place a piece of white paper over them and trace the shape. They can use the traced shape to make a bar graph. If they draw the bars adjacent to one another with no space in between, they have drawn a histogram. Histograms show data grouped in equal intervals. Remind students to give their graphs a title and to label the vertical and horizontal axes. Encourage a discussion of their bar graphs or histograms.

Questions for Students

1. What patterns or clusters do you see in our data?
2. Did other airplanes have about the same median distance as yours?
3. What similarities do other airplanes have with yours?
5. How can we find the median distance for our whole class?
6. What is the mode, or most frequently occurring, distance in our graph?
7. Look at the airplanes that traveled the greatest and least distances. How are they alike? Different?

### Learning Objectives

Students will:

• Collect, organize, display, and interpret data.
• Determine median distances.
• Construct a stem-and-leaf plot of class data.
• Determine the range and mode of class data.

### NCTM Standards and Expectations

• Collect data using observations, surveys, and experiments.
• Represent data using tables and graphs such as line plots, bar graphs, and line graphs.
• Describe the shape and important features of a set of data and compare related data sets, with an emphasis on how the data are distributed.