Mrs. Sweeny`s AP Calculus Final Project Options: 1. Volume Project

Mrs. Sweeny’s AP Calculus Final Project Options:
After a year in AP Calculus AB, each of you has expanded your mathematical knowledge in
ways you may not have imagined possible. As a fun way of capturing some of that knowledge
for posterity’s sake, and possibly pass that knowledge on to future classes, you will complete
one of the projects listed below. Please use your creative talents! You may work either
individually or in a group of two, as desired.
Additionally, each project will be presented to the class under these guidelines:
Delivery: maintain eye contact, speak to the entire audience, do not speak too fast or
too slow, speak so that all may hear, use standard grammar, be clear in your presentation
All partner requests must be made with both students present by 3:00 pm
on Monday, May 11. If no request for a partner is made, it is understood
that the student will work on their own.
All Projects are due on Thursday, May 21, but may be turned in earlier.
1. Volume Project
Make a physical model of a solid with a known cross section on a base with a standard
function(s).
Guidelines:



The base function(s) can be any non-linear function except a parabola, square
root or absolute value. If using more than 1 function for the base, the second
function can be any of your choice.
The cross section can be any shape except a square.
The materials used can be no thicker than 0.25". Your model must be at least 6
inches long and have a minimum of 24 laminations (cross sections).
Presentation must include the following items:





A clear description of function(s) used.
Explanation/sample of what the cross section looks like.
Computed volume for each slice.
Total volume estimate using a Riemann Sum.
Theoretical volume as defined by a definite integral. If your problem is not
integrable, you may use the Numerical Integration feature on your calculator.
Category
5
4
3
2
Difficulty of
Function(s)
Difficult
function(s)
Somewhat
difficult
function(s)
Somewhat
difficult
function(s
Easy function(s)
Difficulty of
Cross Section
Used
Difficult Cross
Section Used
Somewhat
difficult cross
section used
Moderately
difficult cross
section used
Easy cross
section used
Time/ Effort
It is clear that
much time and
effort went into
creating this
project
A sufficient
amount of time
and effort went
into creating this
project
Some time and
effort went into
completing this
project.
Little time and
effort went into
completing this
project.
Usefulness
This project
should definitely
be used next
year to help
students to learn
the concept of
volume of a
solid with known
cross sections
This project
would be helpful
for most
students to
learn the
concept of
volume of a
solid with known
cross sections
This project
might be
beneficial to
some students to
learn the
concept of
volume of a
solid with known
cross sections
This project will
not be beneficial
for students to
learn the
concept of
volume of a
solid with known
cross sections
Correct Calculus
All the Calculus
presented in this
project is correct
Most of the
Calculus
presented in this
project is correct
Some of the
Calculus
presented in this
project is correct
None/a sparse
amount of the
Calculus
presented in this
project is correct
Creativity
Very creative!
Creative
Somewhat
creative
Not very creative
Presentation of
information on
Board
Organized, easy
to understand
Organized, and
somewhat easy
to understand
Somewhat
organized, and
somewhat easy
to understand
Not organized,
not easy to
understand
Required
information on
the board
Includes all
items listed
Missing one item Missing two
items
It is easy to see
that they didn’t
read or adhere
to the list of
what to provide
in the
presentation
Presentation of
project
Members spoke
at a good rate &
volume with
good grammar.
Explanation of
project was clear
and concise
Members spoke
at a fast rate (or
really slow), or
too quietly or
too loudly. They
used acceptable
grammar.
Explanation was
clear
Members spoke
at a good rate
and volume, but
used poor
grammar.
Explanation was
somewhat clear
Members
demonstrated
poor rate,
volume and
grammar.
Explanation was
not clear.
Timeliness
On time
Late – by end of
day
Late – next
school day
Late – after that
Examples:
2. Board Game
You may develop a board game that goes above and beyond the materials students already
have available to them. The criteria are:
 Create a board game where students review calculus concepts. Game play should be
based around answering review questions correctly.
 Minimum board size is 12” x 12”, maximum is 24” x 24”, however, it must fold into a 12”
x 24” size.
 Board must be laminated or of durable material. All accessories must be durable as well.
 The game may be designed to review the entire course, or a particular unit, such as
differentiation or integration.
 The game may be designed to be used by ≥ 2 players
 You may not use a commercially available game as your project. You may, however,
modify an existing board game.
 You game should include a minimum of 40 original question or problems with correct
solutions (at least ½ of the question must be problems).
 Must have clear instructions for play
Category
Game is user
friendly
5
Game is very
easy to
follow
4
Game is
mostly easy
to follow
3
Game is
somewhat
easy to
follow
2
Game is not
very easy to
follow
Compelling
to keep
students
interested
Presentation
Game is very
compelling
Game is
mostly
compelling
Game is
somewhat
compelling
Game is not
very
compelling
Members
spoke at a
good rate &
volume with
good
grammar.
Explanation
of project
was clear and
concise
Board and
pieces are
Members
spoke at a
good rate
and volume,
but used
poor
grammar.
Explanation
was
somewhat
clear
Board and
pieces are
somewhat
Members
demonstrated
poor rate,
volume and
grammar.
Explanation
was not clear.
Materials are
well designed
Members
spoke at a
fast rate (or
really slow),
or too quietly
or too loudly.
They used
acceptable
grammar.
Explanation
was clear
Board is
durable and
well
Neither the
pieces nor te
board are
durable and
designed,
well designed pieces are
not durable
well designed well designed
and durable
and durable
Problems are
interesting
and answers
are correct
All the
Calculus
presented in
this project is
correct and
intriguing
Some of the
Calculus
problems
presented in
this project
are correct
and
intriguing
None/a
sparse
amount of
the Calculus
problems
presented in
this project
are correct
and
intriguing
Creativity
Very creative! Creative
Somewhat
Not very
creative
creative
Usefulness
Time and
effort
This project
should
definitely be
used next
year to help
students to
learn the
concepts
This project
would be
helpful for
most
students to
learn the
concepts
This project
might be
beneficial to
some
students to
learn the
concepts
This project
will not be
beneficial for
students to
learn the
concepts
It is clear that
much time
and effort
went into
creating this
project
A sufficient
amount of
time and
effort went
into creating
this project
Some time
and effort
went into
completing
this project.
Little time
and effort
went into
completing
this project.
Missing one
item
Missing two
items
It is easy to
see that they
didn’t read or
adhere to the
list of what to
provide in the
presentation
Late – by end
of day
Late – next
school day
Late – after
that
Requirements Includes all
items listed
Timeliness
Most of the
Calculus
problems
presented in
this project
are correct
and
intriguing
On time