Math 151-152, Sample Workshop Writeup

Statement of the problem (from Workshop 1, Fall 1998):

A window is in the ``upside-down home plate'' shape of an irregular pentagon, formed by a rectangle surmounted by an isosceles right triangle whose hypotenuse coincides with the top of the rectangle. Suppose that the area of the window is 12 square feet.
(a) Let x be the length of the base of the window and h the height of the rectangle. Sketch the window, labelling all sides, and find an equation relating x and h.
(b) Find a formula for the perimeter p of the window as a function of the single variable x.
(c) Use your calculator to graph the function p=p(x). Are there any upper or lower bounds between which the value of x must lie? If so, decide what happens to p as x approaches those limits, and explain by drawing pictures of the window in those cases.

An excellent sample write-up:

 Some features you should emulate: The writer uses complete sentences. She answers the questions directly. She labels diagrams completely and clearly. When she introduces a new symbol (such as "d" or "AT"), she defines its meaning promptly (and makes sure that the symbol is not already in use). When she invokes a theorem or definition (such as the Pythagorean Theorem), she refers to it by name, avoiding vague references like "By definition" or "By a theorem". She reviews the theorem or definition to make sure that it really applies and that she is using it accurately. She describes calculations in enough detail that a competent reader can reproduce them, but not in excruciating detail (e.g., it suffices to say "Solving for h as a function of x in (4)..." rather than "I subtracted x2/4 from both sides of (4) and then divided both sides by x to obtain..." When she says "clearly", the statement really is clear. She avoids repetition. On the contrary, every sentence contributes something new and important to the chain of argument. The layout is well-spaced and easy to read; important equations are displayed prominently, and labelled if later reference will be made to them.

RNL, 9/29/98