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Deposit # 154

The Classic Volume of a Box

The AP problem behind the movie "Stand and Deliver"

Jaime Escalante

Problems can become "classics" in themselves; thus, a Volume of a Box problem on the May 19, 1982 AP Calculus Exam was, in fact, the very mathematics that led to the fame of Jaime Escalanate and the students of Garfield High School in Los Angeles, California.

Simply stated the problem is as follows:

Volume of a Box: A box with an open top is to be constructed from a rectangular piece of cardboard with dimension 12 in. by 20 in. by cutting out equal squares of side x at each corner and then folding up the sides.

(a) Find a function that models the volume of the box.

(b) Find the valuse of x for which the volume is greater than 200 in3.

(c) Find the largest volume that such a box can have.

This section:  MATHEMATICA® . . .

Escalante: The Best Teacher in America by Jay Mathews, 1988
Escalantese:  A Glossary                         Reproduced from Jay Mathews' book, Appendix 1, p. 307.

Doghouse:  Synthetic Division

Face mask:  A mistake at the problem's beginning

Gravy:  Simple substitution

Green light:  Easy factoring

Red light:  Difficult factoring, stop and study

In love:  Factoring by grouping

Marching band:  A simple solution following usual procedures

Nosey:  Need to study the problem and find the key words

Secret Agent:  The minus sign in front of a parenthesis, with the power to change the signs inside

Thumb up:  A or B

Thumb sideways:  C

Thumb down:  Failing

Rifle pass from Magic Johnson:  Represents another function, a "no look" pass.

All seniors turn crazy:  Reminder of where trig functions are positive (Quadrants I, II,  III, IV).

Students are sent to see:

Dr. White: For a light review
Dr. Green:  For after-school study
Dr. Black:  For emergency treatment and lengthy quarantine

Intensive Care:
When a student is failing test after test, he or she must see Escalante after school every day until improvement shows.

When a student has poor attendance and does not do the required work, he or she must stay after school.