Predicting and Estimating Speeds

and the SR-71


Author: Jodie Johnston, undergraduate student, California Polytechnic State University-San Luis Obispo and Robin A. Ward, California Polytechnic State University-San Luis Obispo


Audience: Grades 4 - 6


Mathematical Topics: predicting/estimating speeds, number sense, converting between and among the metric system and the S.I. system


Rationale: The NCTM Standards recommend that students in grades 4 - 6:

  • develop number sense;

  • estimate and use measurement to solve problems and to check the reasonableness of results;

  • explore relationships between and among numbers.

    • The Standards also recommend that students become actively involved, individually and in groups, in exploring, conjecturing, analyzing, and applying mathematics in both a mathematical and a real-world context.

    This activity provides students with the opportunity to predict and estimate speeds of various familiar, real-world items. In addition, students will develop a sense for the magnitude of numbers by comparing the speeds of these items. Students will also be given the opportunity to convert between and among the metric system and the S.I. (Systeme Internationale) system of measurement. The backdrop for this activity is the SR-71 aircraft, currently being tested at NASA Dryden.


    Background: Two SR-71 aircraft are being used by NASA as testbeds for high speed, high altitude aeronautical research. The SR-71A and an SR-71B pilot trainer aircraft are based at NASA's Dryden Flight Research Center. They have been loaned to NASA by the U.S. Air Force.

    The SR-71, also called the "Blackbird" (because of its color), is the world's fastest and highest-flying production aircraft. The aircraft can fly more than 2200 mph (Mach 3+ or more than three times the speed of sound) and at altitudes of over 85,000 feet. Because the aircraft can fly at such supersonic speeds and at such high altitudes, this operating environment makes the aircraft an excellent platform to carry out research and experiments in a variety of areas including aerodynamics, propulsion, thermal protection materials, high-speed and high-temperature instrumentation, atmospheric studies, and sonic boom characterization. Thus, data obtained from the SR-71 will be used to aid designers of future supersonic/hypersonic aircraft and propulsion systems, including a high speed civil transport.

    View several photos of the SR-71.
    Learn some facts about the SR-71.
    View a movie clip of the SR-71.


    Materials:

    worksheet


    The Activity:

  • Provide the students with some background information on the SR-71. Mention that the aircraft is the fastest aircraft, but do not yet disclose its actual speed. The actual speed will be disclosed at the end of the activity. Show students a picture of the SR-71.

  • Prior to class, the teacher should list on the board up to ten items to be sorted from slowest to fastest. Click here to access a list of several items from which you can choose. The worksheet for students will accommodate up to ten items for students to sort.

  • Place students in groups of two to four. Distribute one worksheet per student. Instruct students to sort the items from slowest to fastest by estimating a speed (in miles per hour) for each of the items. Instruct students to discuss their predictions and estimations with their classmates. Encourage the students to justify their reasoning behind the predictions and estimations.

  • Once each group has reached a consensus on the ordering of the items on the worksheet and each of the items' estimated speeds, provide the students with the actual speeds of the various items. The teacher might want to give prizes to the group(s) of students with the most correct estimations.

  • Allow students time to compare their own lists and estimations with the actual speeds of the items.

  • Now inform students that the speed or the SR-71 is that of a speeding bullet! The SR-71 travels at approximately 2200 mph, or three times the speed as sound (which is referred to as Mach 3). It is hoped that by identifying the speeds of various, familiar items that students will be able to comprehend just how fast 2200 mph is; that is, the speed of the SR-71.


    • Enrichment Activities: Encourage students to compute how many more times faster the SR-71 is than the other items listed on their worksheet. For example:

    If the SR-71 travels 2200 mph, how many times faster is this aircraft compared to a cheetah? Compared to the world's fastest roller coaster?

    The SR-71 is more than 30 times faster than a cheetah since 30 * 70 mph = 2100 mph. To be exact, the SR-71 is 31.4 times faster than a cheetah.

    The SR-71 is 22 times faster than the world's fastest roller coaster since 22 * 100 mph = 2200 mph.

    As another enrichment activity, allow students to search the World Wide Web for the speed of three other items of their choice. Students will record the speeds in their journals. Then, ask students to challenge each other by predicting and recording the speeds of the items found.

    As students search the web, they might find speeds given in the metric system, as oppose to the S.I. system. The teacher might want to introduce and provide students practice with the various conversion formulas when converting between kilometers per hour or meters per second into miles per hour.


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    • Funded by the NASA Dryden Flight Research Center


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