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Table of Contents

1. Lesson Overview
2. Hypertext Outline of Lesson
3. Objectives
4. Time Allotment
5. NCTM Process Standards
6. NCTM Content Standards
7. Aeronautics Content
8. Prerequisite Skills
9. Vocabulary
10. Materials
11. Teacher Tips
12. Additional Activities
13. Accessibility

In the Experimental Department, students are introduced to the process of design testing and evaluation, statistics and data analysis by gathering information about the flights of paper airplanes. Several test flights of a plane are completed and the data is analyzed by finding the range, mean and median of the data. Design changes may be implemented based on the data analysis. Information and values from other sets of data are also displayed in different graphical formats for interpretation.

This purpose of this outline is to help you navigate to specific parts of the lesson without having to go through every page. The section titles link to the first pages of that section, and the numbers in parentheses refer to the page number where that section starts.

• Three Stages of Design (2)
• Sample Size and Bias(5)
• Collecting Data (8)
• Range (9)
• Variation (10)
• Mean (13)
• Median (18)
• Evaluating Your Results (22)
• Straw Glider Results (26)
• Glider Plans (33)

At the end of this lesson, students will:

• Be able to define the three stages of airplane design, design, testing, and evaluation.
• Understand and be able to determine appropriate sample sizes for data collection.
• Understand and be able to define the terms bias, certainty, and variation in statistics.
• Be able to determine the range of a set of numbers.
• Be able to calculate the mean of a set of numbers and understand when it is appropriate to use this value.
• Be able to determine the median of a set of numbers.
• Be able to analyze and evaluate data results using mean, median and range.
• Be able to display, read and interpret data on a number line and a bar graph.

30-40 minutes depending on student's reading ability.

Standard 1: Mathematics as Problem Solving

• Use problem solving approaches to investigate and understand mathematical content.
• Verify and interpret given results and generalize solutions and strategies to a new problem.
• Gain confidence by using math meaningfully.

Standard 2: Mathematics as Communication

• Interpret and evaluate mathematical ideas presented in written and visual forms.
• Discuss mathematical ideas and make convincing arguments.
• Model situations in pictorial, concrete, graphical and algebraic terms.
• Appreciate the value of mathematical notation.

Standard 3: Mathematics as Reasoning

• Understand and apply reasoning to graphs.
• Make and evaluate mathematical arguments about how different values are related to each other.
• Appreciate the power of mathematical reasoning.

Standard 4: Mathematical Connections

• Explore problems and describe results using graphical, physical and verbal math models.
• Apply mathematics to solve problems in science.
• Recognize the value of math in an applied technical situation
• Use mathematical ideas to further understanding of other mathematical ideas.

Standard 5: Number and Number Relationships

• Develop number sense for whole numbers and decimals.
• Represent numerical relationships in 2-dimensional graphs.

Standard 6: Number Systems and Number Theory

• Develop and use order relations for whole numbers and decimals

Standard 7: Computation and Estimation

• Compute whole numbers and decimals.
• Develop procedures for computation and techniques for estimation.
• Select and use an appropriate method for computing.
• Use computation to solve problems.

Standard 8: Patterns and Functions

• Analyze functional relationships to explain how a change in one quantity results in a change in another.

Standard 9: Algebra

• Represent situations and number patterns with tables, graphs, number lines, verbal rules and explore the interrelationships of these representations.
• Develop confidence in solving linear equations using concrete methods.
• Apply algebraic methods tools to solve real world and mathematical problems.

Standard 10: Statistics

• Collect, organize and describe data.
• Read and interpret tables and graphs.
• Make inferences and convincing arguments that are based on data analysis.
• Evaluate argruments that are based on data analysis.
• Develop an appreciation for statistical methods as powerful means for decision making.

Standard 13: Measurement

• Estimate, make and use measurements to describe and compare phenomena.

• Airplane design and test flights
• Air racing

• Students should have some knowledge of calculating the average of a set of numbers.
• Students should have some knowledge of testing or experimental procedure.

• design stage
• testing stage
• prototype
• evaluation stage
• statistics
• sample size
• bias
• certainty
• range
• maximum
• minimum
• variation
• mean
• sum
• median
• bar graph

For helping with calculations:

• paper and pencil, calculator, or an assistive software package such as MathPad

For Straw Glider:

• printer attached to computer
• straw, paper clip, tape and paper

This lesson can be completed individually but will move faster and be more fun if two or more people work together. The lesson can be done in under half an hour if the students are good readers and have a calculator to assist with computations. Pair up students if someone is unable to hold or manipulate objects. Students who are unable to write can provide verbal input on project or make choices during activity.

1. Using the Straw Glider model provided, student can create and conduct their own test flights, gathering and analyzing the data. This can be done induvidually, or in groups. Based on their initial results, have students modify their Straw Gliders by changing the fuselage length, wingspan, or tail size. Then, re-test the glider and compare these results from the original results. What has changed? How might different modifications affect flight?

2. Repeat the above mentioned experiment with each student group creating and testing a different paper airplane. As a whole class, analyze the results from each of the different ariplanes and draw conclusions about patterns, differences and functions of the various parts of the planes.

3. Gather data from other sources (i.e. school sporting events, elections) and analyze them using mean, median and range. What conclusions can you draw from using this kind of data analysis?

4. Have students gather data on each other or on their family members. Be creative and try think of other categories in addition to age, height, weight, etc. What can you find out about your class by analyzing this data?

Do you have ideas for other activities to use with this activity? Send your suggestions to us at planemath@infouse.com.

All the pages maintain a consistent grid of 6 buttons along the bottom of the page, which should be accessible through a ClickIt! overlay for IntelliKeys. For more information on using assistive technology, please refer to the document "Making PlaneMath Accessible" on the main PlaneMath parent/teacher page.

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