Writing in Math Classes
A Guide to Writing in Mathematics Classes
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), 193201.
Below, you can find sets of projects and solutions for PreCalculus, Calculus I, and Calculus II.
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.
Writing Assignments in PreCalculus
by Wendell CulpRessler 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. Rhoda Way flies Quinoa and Aioli to New Guinea. But will she crash and burn at the hands of Dee Seevers?
The first problem graphs a modified trigonometric function. Did Hugh S. Carryman's henchman arrive at the dock when the tide was low or high? 
The first writing assignment is here. 
The second problem optimizes the volume of a box folded from a giant sheet of cardboard. 
The second writing assignment is here. An excellent solution is here. 
The third question compares distance, velocity, and acceleration. Will the runway be long enough that Rhoda and Roger can fly away and escape the clutches of their captors? 
The third writing assignment is here. 
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. 
The second problem optimizes the volume of a small paper bag. It also introduces us to the ohsodreamy Justin Lumberpond (sigh). 
The second writing assignment is here. 
The third problem examines acceleration of a falling object. The exgirlfreind is back and murder is afoot! 
The third writing assignment 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 goodbye letter from Myron is here. 
In this trio of assignments, G. Olson OverbyFitzpatrick, 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 OverbyFitzpatrick 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 OverbyFitzpatrick pack papiermache in his rail cars? 
The second writing assignment is here. 
The third problem compares constant velocity with constant deceleration. Did OverbyFitzpatrick murder Peter Moss by stopping a train? 
The third writing assignment is here. 
In this trio of assignments, Clay Moore (an accidentprone 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 leadglazed mug.
In the first paper, Clay wants to figure out when in the future he should sell his Vase. 

In this paper, Clay needs to determine both the height and the capacity of the Enure Vase. 

In this paper, Clay suffers from a bout of lead poisoning. Is Eve L. Vellen at it again? 
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 rubberstorage 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. 

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. 

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. 
In this trio of assignments, Aloysius Ludwig Thumbs, a freelance 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 firstorder differential equations in the cleanup of a pollen spill. 
The second writing assignment is here. 
The third problem calculates the average height of a weird trapezoidal object; it uses 3d geometry and could involve integration. 
The third 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 3d 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 followup 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 highwire 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