# What Makes Airplanes Fly? History, Science and Applications ofAerodynamics

## CONTENTS OF CURRICULUM UNIT 90.07.10

- Narrative
- I. Introduction
- II. Rationale and General Objectives of the Unit
- III. Historical Overview of the Development of Aircraft4
- IV. The Mathematical Application
- II. An Introduction to Graph Theory
- Sample Lesson Plan 1
- Sample Lesson plan 2
- Sample Lesson Plan 3
- Sample Lesson Plan 4
- Sample Problems For Class Discussion
- Bibliography

### Unit Guide

## Historical Developments of the Aircraft Industry with Mathematical Applications

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## II. Rationale and General Objectives of the Unit

Most of the high school curriculum today has placed great emphasis on the four year college bound student; but there is a growing demand for workers who are literate in mathematics in all sectors of the society.

This unit in aerodynamics will attempt to find the mathematical concepts that are essential to flight with special interest in the concepts that relate to path problems.

The development of this unit will be justified by the emphasis placed on making mathematics relevant, practical and meaningful to the student, thus providing them with answers to “ Why do I need to do this?”, or “ Where in the real world would I ever use this?”

The theme behind the development of this unit is to present mathematical concepts that are not usually taught in the curriculum of students that are labeled low achievers, and to present these topics using flight as the major focus.

It has been a challenge to teach students in the lower mathematics classes. These students have been accustomed to failing the traditional topics such as fractions, and decimals; and in high school they find mathematics difficult, boring and impractical. They have been kept out of the mainstream of mathematics because of their inability to pass the proficiency tests.

In my quest to present these students with mathematics concepts that would otherwise be outside their curriculum, I have attempted to present these topics differently by relating them directly to flight, thus, forging a connection between the historical concepts and some of the mathematics that can be applied to it.

The teaching approach would be to expose these students to the readings of the historical development—(this could be done as a class project or individual students could do research on different areas). The mathematical concepts could be introduced from the view point of students planning a flight in an aircraft then considering the logistics of the flight. Navigation, and spherical geometry could be applied here with the theme: “Planning a Journey.”

The introduction of graph theory could be introduced as a tool to solving problems that relate to the activities that present themselves during the flight; loading and unloading the aircraft; the job activities of the air hostess; even the time line of activities for passengers. Students could brainstorm and develop their own problems.

I share the beliefs presented in the Mathematics Standards prepared by the N.T.C.M.,
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that mathematics should be made relevant, that its application should be shown across subject areas, and that all students can be successful in mathematics.

### General Objectives of the unit

The unit will be designed to help students:

- a) To acquire knowledge about the historical development of the industry
- b) To develop the ability to apply their knowledge in math to the task of problem solving.
- c) To apply specific graphing skills to solving problems
- d) To use Graph Theory to solve problems related to paths.
- e) Introduce students to Spherical Geometry as a link between Geography and Geometry.