Building a Catapult
by Stephen Alwon and Sherwin Fernandes
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SUMMARYMathematics
in AISD is taught for the most part as a series of lectures disparate from
everything else the students learn in their other classes. In using a project based around designing a
catapult, students will be able to see mathematics come to life in a manner
that brings together physics, engineering, and history in a way that they
have not seen before. The students
will participate in a series of labs during which they will construct both
the basic theory of projectile motion and the basic principles and behavior
of quadratic functions. Students will
then be able to put their knowledge to use by building a working catapult and
rationalizing how far it will launch a ball.
Through this project, the students will be able to bring together mathematics
and physics in a manner that will enable them to solve a problem that has
been around for thousands of years, giving them a historical background for
their project. Additionally, the
students will have a working knowledge of the basic concepts of physics,
allowing them to be better prepared when they enter a physics course. Finally, the project will be fun, and will
encourage students to think deeply about mathematics because they want to,
not just in order to pass a test or so they can graduate. DESCRIPTIONThe projectile launching project is primarily about applying concepts on such as forms of energy and conservation of energy, as well as acceleration due to gravity and inertia. To aid in the usage of these ideas the final lab on building a projectile launcher is precluded by several learning activities on the required topics. To
understand how energy is stored in a spring students will first measure the
variation of the length of a spring with force. This will be done by hanging
a spring from a stand, applying different weights to the free end and
measuring the extension of the spring with a ruler. To calculate how much
energy is stored in the spring, students will count energy as Newton-meters
and find out how many Newton-meter boxes are under the force distance graph. To
study projectile motion students will use a stroboscope and extended exposure
camera to record the path of a falling ball. Images of the parabolic path
will be used to study the linear nature of the horizontal component of motion.
The vertical fall will be used to study how the distance traveled is
proportional to the square of time. To
predict how far the projectile will travel, students will take readings from
a projectile-motion applet. Students will record how the distance traveled by
a projectile will vary with the speed and angle it is launched at. The data
will be combined into a 3-D curve (using a math computer tool). To
demonstrate that the energy with which the ball is launched is transferred
over its flight, students will observe the conservation of energy in a
falling ball. A motion detector placed below a ball will record the height
and speed of the ball as it falls. These will be used to calculate the
kinetic and potential energies and how they add up to the same amount
throughout. The
main lab will incorporate data and concepts acquired in previous labs into
the design of the projectile launcher. Students will consider the most energy
and cost efficient way to transfer the projectile from the launch base to the
given target. Once students have designed their launchers they will construct
them using an erector set and springs. They will then predict where the ball
will land using information gathered in previous labs. When
the launchers have been built and tested, each team will present their
findings and discuss design and implementation aspects of their project. RATIONALEOne
of the main problems with the way mathematics is taught in AISD is that it is
taught in a vacuum, with rarely any connection being made between the
mathematics classroom and any other class they are taking. Students are made to forget everything they
learned during the previous hour and start entirely fresh when they enter
their mathematics class. With this
project, students will bring together concepts from various subjects such as
engineering, physics, and history while they are learning mathematics. The problem of how to best launch a
projectile is one that has been around for hundreds of years, and students
will be able to see this problem come to life in their world history
class. The ability to bring together
mathematics and history will encourage students who are interested in either
subject to seek out the other.
Students will discover how wars were fought for thousands of years, making
the problem of how to build a working one relevant to students who enjoy
history and social studies, while students who enjoy mathematics and the
sciences will be able to see the social studies in a new light. The project will also introduce students to
the engineering process, from learning the necessary physics and mathematics
to designing and constructing a working catapult. POTENTIAL IMPACTOur
project will attempt to get students interested in mathematics by bringing
other disciplines into the mathematics classroom. In this way, students will be able to see
how mathematics can relate to subjects they most likely will not have seen a
connection to before, such as history.
Students will be motivated to learn the mathematics not necessarily
just to learn math, pass a test, or graduate high school, but as a way to
better understand how history was shaped for hundreds of years. Students whose primary scholastic interests
were in social studies before participating in the project will have a
different outlook on mathematics and the ways it can be used. In this way, these students will have a new
appreciation for mathematics and will be more excited to participate in math
classes in the future. Conversely,
students whose main interests lie in the sciences will have a new outlook on
history, and will be more excited to participate in those classes. Our project will also prepare students for
when they take physics by introducing them to some of the more basic concepts
they will learn in that class. This
will enable the teacher who has these students to save time in covering some
of the basic concepts, and instead allow them to spend more time on the
concepts that the students have not been presented previously. EVALUATION PLAN Our
project will depend on two main techniques for measuring the progress of our
students. The first will be the labs
and homeworks which will be assigned on a regular
basis. The labs will be done mostly in
class, with the students able to finish outside if necessary. Through these, the students will be able to
witness first hand the physical and mathematical concepts they are to learn,
and successful completion of the lab write-ups will depend on them thoroughly
understanding the concepts the labs are designed to exhibit. These will let us know that the students
are working during class time and that their work is productive. The homeworks
will be designed to evaluate the concepts that are more mathematical in
nature – problems such as finding quadratic roots. These will enable us to quickly judge if
the students are “getting” the mathematical concepts involved in
the project. The other evaluation
technique will be through the final project itself – each group’s
design of the catapult and their rationale of why their catapult works and
how far they expect it to shoot. This
will allow us to determine how well the students brought together all of the
concepts involved and how well they are able to communicate their knowledge
of those concepts. PROJECT CALENDAR
BUDGET
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