Illuminations: Long Distance Airplanes

# Long Distance Airplanes

 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.

### 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

### Materials

 Paper for making airplanes Rulers Yardsticks or measuring tape How Far Can Your Airplane Travel? Activity Sheet

### Questions for Students

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

### Assessment Options

 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. 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

 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. 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.

### NCTM Standards and Expectations

 Data Analysis & Probability 3-5Collect 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.

2 periods

### Lessons

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