Math tutorials for budding activists

My daughter, now in grade 9, is learning to do linear equations in her math class, then mapping points as Cartesian co–ordinates on graph paper. She’s a reasonably bright 14-year-old, but no math whiz, mostly because she feels no motivation to learn the problems. How do they relate to real-world issues? It’s amazing that this math has been with us for only 375 years. It took the greatest mind of the early 17th century to come up with the idea, and even then Descartes couldn’t have invented it without the work of Vieta a century earlier. It was Vieta who invented the idea of X—the use of variables in algebraic notation. But Descartes could only imagine his co–ordinates in one quadrant—using positive numbers. It took one of the greatest minds of history, Isaac Newton, to realize that if you used the set of all real numbers, then the co–ordinate system can have four quadrants with 0,0 at the center. Now, we expect the average 14-year-old to understand concepts which—for most of human history—teenagers managed to live comfortably without.

The issue is relevance. As I sat with my daughter at the kitchen table, trying to ease through a problem about a car driving from boring points A to B to C, I noticed how her eyes glazed over. It was time to spice up the problems. You’ve heard of the School of the Americas? Where CIA operatives train thugs to “manage” populations in less enlightened countries? What about a school of the Canadas? Where kids can learn the three R’s while incidentally developing a motivation for subversion. So I came up with a few math problems as my little contribution to a revised grade 9 curriculum.

1. The average corporal in the U.S. marines, when wide awake and jacked with 7 cups of coffee, can lead a technical team in operating an Expeditionary Fire Support System (mobile units for firing large mortar shells) at a rate of 6 shells each hour. These are supposed to be precision targeted to limit collateral damage to 7 civilian casualties/hour. But as the day wears on, the team suffers from fatigue, and precision suffers accordingly. If the team starts shelling targets at 6:00 with 7 civilian casualties per hour, with accuracy deteriorating to 12 casualties per hour at 9:00 and 17 casualties per hour at 12:00, answer the following questions:

(a) Develop an equation that relates time spent shelling to civilian casualties.

(b) Use your equation to predict the number of civilians killed between 18:00 and 19:00 hours.

(c) If the team stops shelling at 21:00, what is the total number of civilians dead for the day?

(d) Graph the equation in (a).

(e) What number set are you using? Real? Unreal? Completely irrational?

2. In sub-Saharan Africa, more than 3 million people died of AIDS last year. Assume the following facts for this problem:

• assume that these deaths arise from a population of 40 million people who are HIV+
• assume rates of new infection are currently increasing annually at 10%
• assume that an expenditure of US$2 billion on drugs and education could reduce rates of new infections by 50 %

Answer the following questions:

(a) If we did nothing, how many people would die in year five?

(b) If we spent US$2 billion, how many people would live in year five who otherwise would have died?

(c) Last year, NASA spent US$ 900 million repairing the Hubble space telescope? How many people in sub-Saharan Africa will die this year so NASA can take nice photos of objects 10 billion light years away?

(d) Last year, a consortium proposed an ELT (Extremely Large Telescope) to be installed in the Antarctic for US$1.3 billion. How many people could be saved this year if such an expenditure were applied to treatment and education of HIV/AIDS victims instead?

3. Experience at the WTO meetings in Seattle taught protesters that a typical 500 mL spray can costing $12.95 will empty completely after 5 minutes of continuous spraying. However, the typical protester’s index finger starts to cramp and so each subsequent spray can takes a minute longer to empty than the previous can. You are planning to spraypaint limos at the next G8 summit. You have learned that G8 leaders and their staff use a total of 100 limousines. On any given evening, at least 14 of those limousines are transporting leaders and their staff to Madame Mersault’s. Assume all Johns stay for a half hour (busy schedules) and pay $100. Assume it takes you 10 minutes to bribe each driver at a cost of $60 before you can begin to work on a car. One car arrives, drops off a leader or staff member, waits until the job is done, then leaves as the next car arrives …

(a) Develop an equation to relate the use of cans over time.

(b) After the first car, who has paid more for their fun, you or George W. Bush?

(c) If you were working with a partner, and you found all 100 limos parked together at a downtown hotel, how long would it take you to decorate all the cars?

(d) How many litres of paint would you have used?

4. In Guantanamo Bay, a guard’s punch will typically land with a force of 3200 Kg/cm2 and knock out one tooth. But it only takes an additional 800 Kg/cm2 to knock out two teeth. Very little additional effort yields fantastic results, with a further 200 Kg/cm2 typically knocking out three teeth.

(a) Graph a straight line to see if this reveals any trend.

(b) Try to predict how many teeth a detainee would lose if his guard punched him in the mouth with a force of 5000 Kg/cm2.

(c) Assume that each detainee began with a full set of teeth (32) and 10 guards typically strike detainees in the mouth with a force of 4000 Kg/cm2 each day. If there were 1,000 detainees, how long would it take for all the detainees to lose all their teeth?