Develop and appreciation for geometry as a means of describing the physical world.
Facility with a protractor is important in developing the concepts of "angle" and "angle measure." Hands-on experience with a protractor helps the students to begin to visualize geometric relationships and assists them in making realistic estimations as a means of problem solving. This activity provides students with a real-life situation in which angle measurement is readily seen.
Background: The
NASA Dryden Flight Research Center
located at Edwards, California has been on the forefront of aeronautical engineering for over 50 years. The engineers at NASA-Dryden research and test a wide variety of different types of aircraft. They are constantly striving to achieve optimal efficiency of each aircraft for its specific use. To do this, the angles of wings and tails are frequently adjusted.
In this activity, students will use a protractor to measure the angles of wings and tails of various different aircraft to demonstrate the diversity in aircraft engineering. Students will have the opportunity to first estimate and then check their estimations. Students will be introduced to the following terms with regard to angles: perpendicular, acute, obtuse, congruent, adjacent, complementary, supplementary and straight angles. While estimating and measuring angles, students will also learn about various aircraft being developed and tested at NASA Dryden and how these aircraft are advancing our knowledge in terms of scientific and aerodynamic research.
Materials:
overhead transparency of
F-15 Active. (Also make hard copies for students to use as a practice worksheet.)
protractors
overhead marker
Students will also select 3 drawings from the following list of NASA Dryden aircraft (in addition to the F-15 Active that is used as the model by the teacher):
HiMAT
F-8 Crusader
F-16A
F-18A
X-15
YAV-8B "Harrier"
YF-12A
The Activity:
Allow the children a few moments to explore their protractors. They may examine them, trace, or draw lines with them. Following the exploration, ask the following questions:
For what purpose do you think the protractor is used?
How do you think the measurement is done?
Explain that aeronautical engineers must use protractors all the time to determine the exact angles of the wings on their aircraft. The students are going to evaluate some of these angles by using their own protractors with line drawings of different NASA-developed aircraft.
Using the drawing of the F-15 Active on the overhead, the teacher will demonstrate how to use the protractor to measure the angles of the wings. The class should follow along using their copy of the diagram. The F-15 Active has wings and a tail that stand at nearly 90-degrees. Discuss what it means to be perpendicular.
Two lines are perpendicular if they intersect at right angles. Right angles measure 90 degrees.
Holding the protractor on the plane, the students can see that the wingspan lies at 180-degrees. Discuss the term straight angle.
A straight angle is an angle that measures 180 degrees.
Next, define supplementary angles.
Supplementary angles are angles whose sum is 180 degrees.
Ask the students to look at the angles on each side of the tail. How do they relate to each other? Explain how these angles are adjacent to each other, and that they are also congruent.
Two angles are considered to be adjacent if they share a common side.
Two angles are congruent if they have the same measure.
Next, each student will have the opportunity to select 3 other aircraft drawings to measure. Before measuring these angles, the students should record an estimation of the angle of the wings of their aircraft. Next, they will check their estimations by actually measuring the angles with their protractors. Students should record actual measurements.
Students can next compare their results with at least 3 other classmates. Allow students to also examine the work of other students who measured different aircraft.
Follow up with an entire class discussion on each of the different aircraft. Discussions can be generated involving the characteristics of the individual aircraft. For instance, the YAV-8B "Harrier" is a nice example of obtuse angles, as well as the F-8 Crusader.
An obtuse angle is an angle that has a measure greater than 90 degrees but less than 180 degrees.
Acute angles can be found on the HiMAT, F-18A, and on the underside of the X-15.
An acute angle is an angle that has a measure greater than 0 degrees but less than 90 degrees.
The YF-12A has smaller sets of angles within the 180-degree wingspan. Which of these are congruent?
Have the students compare the results of their collective work. How close were different students' measurements of like aircraft? Who found angles on their aircraft in places other than the traditional wingspan? What was their measure? Can the students take a guess at what those other angles or small wings/tails might be used for (i.e. stabilization, aerodynamics, etc.)?
Enrichment Activities: There are many other aircraft line drawings available through the NASA Dryden Flight Research Center. Students may choose to locate two or three of these drawings for additional measurement activities and then share their newly acquired information with the class after measuring the angles in new aircraft.
Students might also link to below listed web sites to read and learn some NASA Facts about the various aircraft.
X-15
HiMAT
Students can watch movie clips of the following aircraft:
F-16A
X-15
YF-12A
Students can view more photos of the following aircraft:
F-8C Crusader
F-15 Active
F-16
X-15
YF-12
Students can also use their protractors to measure various objects in the classroom. Challenge students to find and record examples of adjacent, perpendicular, and supplementary angles in objects in the classroom or at home.
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Math Activities for Grades 9 -12
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Funded by the
NASA Dryden Flight Research Center
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