• A nice percents problem: cut emissions to A% below today's
Vs. cut emission to B% below 1990 levels.
• Related percents problem: What percent cut per year
(e.g. r^n = (0.6), find r)
Back to "cut emissions by N% in Y years"
Is it enough to agree on N and Y?
..almost everyone now agrees that we must act..If we're to have a high chance of preventing global temperatures from rising by 2C (3.6F) above preindustrial levels, we need, in the rich nations,A 90% reduction in greenhouse-gas emissions by 2030. The greater part of the cut has to be made at the beginning of this period. To see why, picture two graphs with time on the horizontal axis and the rate of emissions plotted vertically. On one graph the line falls like a ski jump: a steep drop followed by a shallow tail. On the other it falls like the trajectory of a bullet. The area under each [curve] represents the total volume of greenhouse gases produced in that period. They fall to the same point by the same date, but far more gases have been produced in the second case, making runaway climate change more likely. -George Monbiot writing in The Guardian, 10/31/2006
♦ Quadratic and root functions -- wind speed versus
kinetic energy of storm. Area swept out my blades of wind
turbine. Trying to save time by going over the speed limit
(Limited coverage!)
♦ Exponential functions
• Finding average annual growth rates given beg./end values;
• Extrapolation to future (oil consumption, other resources,
Dow Jones in 2100,..) ; Personal financial planning, etc.
Q:
The world currently uses up ≅85 million barrels of
oil per day. If the total remaining oil reserves ≅ 1 trillion
barrels, how many more years do we have before we run out?
"A":
(85,000,000 barrels/day) · (365 days/yr) = 31.025 billion bbl/yr
#4 Physical reality of oil fields.
• Similar: Canadian Tar Sands won't save us from Peak Oil
Challenges of the course
♦ Heterogeneous levels of motivation (somewhat) improved by
env. interest on the part of many (most?) students.
"I don't like working in groups, so I stopped coming to class"
• Freedom-to-choose and Open-ended assignments: Journal, Project
(despite detailed rubric given out; offers to meet groups;
offers view drafts, etc)
• Open-ended questions included on HW ("How
would you generalize? Can you think of other examples?" etc)
"I was able to see how to use math. In other math classes
they throw formulas at you. Here, we took those formulas and actually
used them in life" (Course eval in one section)
"This course was an exception for me..I have always disliked
math for two reasons: I felt that math used extremely complicated
methods and formulas to solve problems that I felt were insignificant
and impractical. This course proved to be the opposite in which
simpler math was used to solve significant, impacting world issues.."
(PEMJ, student in a different section)
"I learned some things that will be pretty useful in the future.. a
lot of it was common sense" (eval)
"The course was challenging, but ultimately improved my
understanding of mathematical concepts" (eval)
"..the area under the curve of a graph represent an amount if [y-axis
quantity] is a rate. In addition, you can [estimate] the area under
the curve without using calculus! You can estimate using lots of
skinny rectangles" (PEMJ)
Oil fields ≠ a gas tank
•Simplified analysis w/piecewise-linear graphs; Given
½b·h, find b.
♦ Very heterogeneous math backgrounds:
→ "It was ok. The teacher was nice, but I have a very hard
time with math"
and "The material that was covered was very difficult"
→ versus "The math was pretty easy"
"very basic, but it was good for the students who were totally anti-math"
Median # of hrs (self-reported!) spent outside of
class per week? 2½ (should be 6). Higher? during Projects
(mandated group work Log)
♦ Student feedback/complaints/compliments
Other Complaints = Some students' Compliments =