Plan #12 - Parametric Arrows
By Timothy J. Cody
and arrow have a rich history among the Native American and its use
as a tool for hunting and a weapon of defense or war. Many lessons can
be created to include the use of the bow and arrow into a variety of
curriculums. Among some of the curriculums that could utilize the bow
and arrow in various units could be: Art, Social Studies, Language Arts,
Physics and Mathematics.
For the students to connect with the use of the bow and arrow for hunting
among the Native Americans and apply it to properties of Physics and
parametric equations to be used in Calculus. Included in the lessons
would be several of the National Council of Teaching Mathematics Standards,
which would be applied with the lessons.
Depending on the depth of each curriculum's lesson, the one involving
the team effort of Physics and Calculus could be 2-3 weeks.
Computers with Internet access, Ti graphing calculators, Vernier products
CBL (calculator based laboratories) and photo gates attachments, bow
and arrows, targets, measuring tapes
Students will first be asked to keep a journal of their work to include
in a report on the total experiment and all related work. Students will
need to connect with an on-line sight in the Internet to download programs
for photo gates with CBL units and the Tt calculators. Students will
then be ready to set up CBL and photo gates on a course with a target
approximately 50 or 100 meters away. Photo gates will be placed on the
ground to record various intervals during the flight path of the arrow
from which data points will generate a parametric equation. This equation
will be used to further explore concepts of vectors in Physics and derivatives
in Calculus. Needed will be preliminary calculations for the height
of targets and release points of the arrows. This will be done with
the tape measures as well as the distances between the targets and release
points. From this also will come data collected to map out the path
of the arrow on grid paper with a rectangular coordinate system. In
addition to the data collection and calculation work, there will also
be presentations by Native American community resources giving talks
on the construction of the bow and arrows in traditional fashion as
well as a bit of historical background on the cultural uses of these
National Standards for Mathematics, the following would be covered in
this lesson: Standard 1-Mathematics as Problem Solving with investigation
application, recognition, formulation of real-world situations of this
experiment; Standard 2-Mathematics as Communication with reflection,
journalizing, formulating, expressing, extending, and appreciation of
the process involved; Standard 3-Mathematics as Reasoning with testing,
conjecturing, constructing, and formulating assertions of this exploration.
Standard 4-Mathematical Connections with the relation of math to the
flight and properties involved in shooting a bow and arrow.
Standard 5-Algebra with both calculation work and equations for Physics
and Calculus topics; Standard 6-Functions with real-world situations
involving graphs tables and parametric changes.
For each particular discipline, a variety of methods of assessments
could be used from the proper use of technology and the ability to use
and set up equipment and materials to the correctness of grammar in
journals. A whole host of things could be evaluated from this project
and its different concepts available to be taught.