# 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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## Sample Lesson Plan 4

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Topic: Introduction to Vectors as a means of representing a distance.
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Objectives: Students will be able to
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- a) Describe a position relative to a point.
- b) To write the coordinate of a point in the coordinate plane.
- c) Write the coordinate as a vector.

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Prerequisites:
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- 1. To plot points in the coordinate plane.
- 2. To use a protractor to measure an angle.
- 3. To draw to scale.

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Skills and Concepts presented:
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- 1. Drawing angle bearing.
- 2. Writing coordinates with distance and angles.
- 3. Plotting a position in the coordinate plane using direction East and North.
- 4. Reading and writing the position as an ordered pair (length, angle) and as a vector (East, North).

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Development:
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- 1. Review angle measure (bearing).
- 2. Introduce the use of a scale (model drawing)
- 3. Using the picture in the content, have students give the position of the boat using the format (length, angle). Have students draw other positions using variation of the angles and lengths.
- 4. From the coordinate system shown have students give the position of the ship using ordered pairs, (East, North).
- 5. Introduce Vectors as a means of writing a displacement.
- 6. Work with students in writing the displacements. For example, suppose the ship moved from position S and Its movement is (2/6), then its position relative to the port will be (4/3) + (2/6) = (6/9). Have students represent this position on their graph paper.