with

Dr. Annalisa Crannell

Franklin & Marshall College

"Please feel free to use these materials with proper citation. If you do adopt or adapt any of these, please let me know at Annalisa.Crannell@FandM.edu."

Jump down to:

• Materials for Getting Started •

Writing Assignments in . . . Calculus I • Calculus II • Calculus III

Materials for Getting Started

A Guide to Writing in
Mathematics Classes

(html
version

(pdf version, 56 KB,
thanks to Lee J. Stemkoski of Dartmouth)

Checklist for writing
and grading essays

For more information, see Crannell, Annalisa, "How to Grade 300 Mathematical Essays and Survive to tell the Tale," PRIMUS 4, 3 (1994), 193-201.

Tommy Ratliff (Wheaton College)

Gavin LaRose (Nebraska Wesleyan)

Sandefur and Dance (Georgetown: these are hands-on algebra & precalc activities)

Field-tested
Learning Assessment Guide for
science, math, engineering, and technology instructors

The Calibrated
Peer
Review site supports student reviewing/grading of
assignments.

My Old Assignments (PreCalc to Calc III)

by Annalisa Crannell unless otherwise noted

Writing Assignments in PreCalculus

by Wendell Culp-Ressler and Annalisa Crannell

Paper 1: The Case of the Nice, Cold Beer

concept: creating and interpreting graphs

Paper 2: The Case of the Perfect Cans

concept: finding extreme values given a constraint

The latest, emerging saga. Tara Nova cleans
salad jars and bags up spices. Will she find true love as
well?

The first problem compares
linear with exponential functions. Should Tara wash a
jar twice with a lot of water each time, or many times with
small amounts of water? |
The first writing assignment
is here. An excellent solution is here. |

The second problem optimizes
the volume of a small paper bag. It also introduces us
to the oh-so-dreamy Justin Lumberpond (sigh). |
The second writing assignment
is here. An excellent solution is here. |

The third problem examines
acceleration of a falling object. The ex-girlfreind is
back and murder is afoot! |
The third writing assignment
is here . An excellent solution is here. |

In this trio of assignments, Myron Sopher finds his beloved Philomena after years of separation. But will he get his girl, or will he lose her to his rival, Victor Dendron?

The first problem uses exponential functions; it requires technological help in the solution. How much money was put into the bank, and what was the interest rate, if we know how much money we made in the short and long run? |
The first writing assignment is here. |

The second problem optimizes the cost of a box that requires soldering. How should we build a storage box the most cheaply? |
The second writing assignment is here. |

The third problem looks at acceleration due to gravity (and maybe air resistance?). Did Victor Dendron conspire to murder Gus Gusterson? |
The third writing assignment is here. |

And just because many of my
students wanted to know: Did Myron get his girl? |
A good-bye letter from
Myron is here. |

In this trio of assignments, G. Olson Overby-Fitzpatrick, a railway owner, needs help with combating speeding tickets, packing problems, and murder charges. We discover he's not a very nice man.

The first problem uses one of my favorite problem contrasting average velocity with the average of several velocities. Does Overby-Fitzpatrick deserve a speeding ticket? |
The first writing assignment is here. |

The second problem optimizes the center of mass; surface area and volume of rectangular objects play an important role. How high should Overby-Fitzpatrick pack papier-mache in his rail cars? |
The second writing assignment is here. |

The third problem compares constant velocity with constant deceleration. Did Overby-Fitzpatrick murder Peter Moss by stopping a train? |
The third writing assignment is here. |

*Alas, I assigned the papers below so long ago
that I do not have electronic versions of the solutions to
these. But they're fun papers nonentheless.*

**First Semester**: George is snookered by the
evil Jack Phaze; he saves his greenhouse from financial ruin and
learns to measure leaves. Meanwhile, his employees win the track
relay.

- How many
trees fit in a greenhouse?

concept: creating and interpreting functions - The Area of
Leaves

concept: Riemann Sums - The Case of the
Dropped Baton

concept: constant speed versus constant acceleration

**Second Semester:** The Saga continues as Joe
Merton discovers that grapefruits can only fall so fast; the
evil Jack Phaze returns as a potential murderer; and Joe is
saved just in time to fall in love with his doctor.

- The Case of
the Falling Grapefruit

concept: differential equations; using initial values to find exact solutions - The Case
of the Lead Poisoning

concept: writing coupled differential equations and solving them - The Case
of Darlene's Rose

concept: Finding limits of integration and areas in polar coordinates

The Case of the Dead
Doornail

concept: average velocity vs. the average of velocities

The General Spore

concept: modeling exponential growth and rate of change

The Case of the Fall from
Grace

concept: motion and timing of a falling body

In this trio of assignments, Clay Moore (an
accident-prone pottery worker) helps his boss figure out selling
strategies for the enormous Enure Vase . . . and then suffers
injuries involving aluminum ladders, roller skates, a bucket of
tennis balls, not to mention a lead-glazed mug.

In the first paper, Clay
wants to figure out when in the future he should sell his
Vase. This paper uses the Fundamental Theorem of Calculus, the product rule, and graph-reading skills. |
The first paper is here. An excellent
solution is here. |

In this paper, Clay needs to
determine both the height and the capacity of the Enure
Vase. This paper uses volume of solids of revolution and Riemann Sums. |
The second paper is here. An excellent solution is here. |

In this paper, Clay suffers
from a bout of lead poisoning. Is Eve L. Vellen at it
again? This paper uses coupled linear differential equations. |
The third paper is here. |

In this trio of assignments, William Avering (a vacillating shoe
manufacturer) tries to make good decisions about buying and
selling rubber-storage containers . . . and then is diabolically
trapped in his own storage tank. This trio has some of the
most unforgivable puns that I have yet used in paper
assignments.

In the first paper, W.
Avering wants to figure out when he should have sold his
rubber making equipment to have maximized profit. This paper uses the Fundamental Theorem of Calculus, the product rule, and graph-reading skills. |
The first paper is here. An
excellent solution is here. |

In this paper, Avering tries
to determine the shape of the storage tank that Eve L.
Vellen sold him. If he's wise, he'll calclulate
volumes using integration and solids of revolution. |
The second paper is here. An excellent solution is here. |

In this paper, W. Avering is
trapped in an underground chamber using methods that are
half Batman, half Rube Goldberg. Solving the problem
requires both infinite series and understanding of the
motion of falling objects. |
The third paper is here. An excellent solution is here. |

In this trio of assignments, Aloysius Ludwig Thumbs, a free-lance home repair technician, needs help with various home improvement projects. Poor Al is constantly beset by unfortunate accidents.

The first problem uses geometry and optimization to design a greenhouse. |
The first writing assignment is here. |

The second problem uses first-order differential equations in the clean-up of a pollen spill. |
The second writing assignment is here. |

The third problem calculates the average height of a weird trapezoidal object; it uses 3-d geometry and could involve integration. |
The first writing assignment is here. |

In this trio of assignments, Brent Trachte, the
ethically dubious turkey farmer, needs help with his water
tanks.

The first problem uses Riemann sums to find the volume of a (somewhat) cylindrical object. |
The first writing assignment is here. |

The second problem has students determine the areas of slices of a circle, in order to find the volume of water in his cylindrical tank. |
The second writing assignment is here. |

The third problem (which is almost calculus III material) uses 3-d geometry and arclength to solve a problem with the intersection of two cylinders of different diameters. |
The third writing assignment is here. |

After all the work they did
to help Brent, students get a follow-up letter from the
law. |
Here is advice
to stay away from Brent! |

In this trio of papers, Matilida Majestica has
trouble at the *Search Us Circus*.

The first problem deals with catenaries (is her high-wire made of titanium or aluminum?). |
The first writing assignment is here. |

The second problem cools a large amount of jello (using Newton's Law of Cooling). |
The second writing assignment is here. |

The third problem deals with attempted murder by rhinoceros (using damped oscillators and 2nd order differential equations). |
The third writing assignment is here. |

*Alas, I assigned the papers below so long ago
that I do not have electronic versions of the solutions to
these. But they're fun papers nonentheless.*

The Case of the Jiggling
Jello

concept: Newton's Law of Cooling

The Case of the Murky
Well

concept: calculating volumes of solids of revolution [with
thanks to Cohen, Gaughan, Knoebel, Kurtz, and Pengelly, *Student
Research Projects in Calculus,* Washington DC: MAA (1991)].

The Case of the
Crushed Clown

concept: projectile motion

The Case of the Space
Signal

concept: Taylor's series approximations of e and [with
thanks to Cohen, Gaughan, Knoebel, Kurtz, and Pengelly, Student
Research Projects in Calculus, Washington DC: MAA (1991)].

The Case of Dome Luck

concept: method of parallax; equations of surfaces [with thanks
to Tom Rishel, Using Writing to Teach Mathematics, MAA Notes
16...(details to be supplied soon)].

The General Spore

concept: Lagrange Multipliers

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• Materials for Getting Started •

Writing Assignments in . . . Calculus I • Calculus II • Calculus III

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