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 PREP 2012
"The MAA is proud to offer a broad range of professional development
opportunities for those teaching and working in the mathematical sciences.
PREP workshops are participatory and interactive, and strive to, and serve
mathematicians at all stages in their careers. Each workshop is an extended
professional development program that includes a preparatory, intensive, and
follow-up component." (MAA PREP Brochure)
A limited number of travel grants are applicants who demonstrate that their
participation in PREP workshops will result in activities at their home
institution that are recognized as immediately relevant and of value to their
departments. The 9 PREP workshops offered this summer are:
1. A New Approach to Intermediate
and College Algebra
Don Small and Erick Hofacker
June 4-8, 2012
2. Improving College Mathematics
Teaching Through Faculty
Gerald Kobyiski, Hilary Fletcher,
June 10-15, 2012
West Point, NY
3. Supporting Research For Teachers
of Post-Calculus Students
Caren Diefenderfer and Dan Teague
June 18-22, 2012
4. Using Inquiry Based Learning in
Second-Year Calculus For
Doug Moore and Bill Jacob
June 19-22, 2012
Santa Barbara, CA
5. Do-It-Yourself (DIV) Modeling
Elizabeth Yanik, Frank Wattenberg,
Gregor Novak, Joe Yanik
June 25-29, 2012
Cocoa Beach, FL
6. Modeling: Early and Often in
Daniel Kaplan, Randall Pruim,
Eric Markland, Nicholas Horton
July 9-13, 2012
Grand Rapids, MI
7. Teaching That Emphasizes
Mathematical Practices for
Phyllis Chinn and Dale Oliver
July 15-20, 2012
8. Beyond Introductory Statistics:
Generalized Linear and
Jim Albert and Brad Hartlaub
July 16-20, 2012
9. (Online) Sage: Using Open-Source
Mathematics Software with
Karl-Dieter Crisman and Dan Drake
June 26, July 10, 17, and 24, 2012
To register or learn about the workshops, visit www.maa.org/PREP.
 Fun Project: Pascal's Triangle
The history of Pascal's Triangle predates Pascal by several centuries. The earliest explicit illustration of the Triangle was in the 10 century commentaries on Chandas Shastra, a 2 century BC book by Pingala on Sanskrit prosody. The Triangle may have originated from a study of binomial expansions as the entries in the row are the coefficients in the expansion of (). Relations among the entries of the Triangle have been discovered and rediscovered many times and in many different countries which has resulted in different names attached to the Triangle. For example, in Iran the Triangle is known as the Khayyam Triangle in honor of the Persian mathematician Omar Khayyam (1048-1131) and in China the Triangle is called Yang Hui's Triangle in respect for the work of Jia Xian (1010-1070) and in Italy the Triangle is referred to as Tartaglia's Triangle in recognition of Niccolo Fontana Tartaglia (1500-1577). The current (Western) name was given by Pierre Raymond Montmort (1708) in recognition of Pascal's book (1665) entitled Treatise on Arithmetical Triangle in which he collected and organized the known relations among the entries in the Triangle. (Source: Pascal's Triangle, wikipdeia.org)
Rows 0 - 4 of Pascal's Triangle are displayed here. The top row is row number
Note that the outside diagonals are all 1's and each interior entry is the sum
of the two entries in the previous row one to the upper left and one to the
Some activities to be explored in developing a small group, Fun Project on
1. Construct the
row of Pascal's Triangle.
2. Show that the entries in the third row are the coefficients in the
3. Show that the sum of the entries in the row is
4. Illustrate and then explain why the number of combinations of
at a time,
is the entry in the
5. Explain why the second diagonal is the set of natural numbers, the second
diagonal is the set of triangle numbers, and the third diagonal is the set of
6. Consider each entry as a node in a grid which is connected to the adjacent entries above and below (but not horizontally). Illustrate that an entry is the number of paths connecting that entry with the top node (1).
 Shrinking Value of the Dollar
The following table shows the amount of money that is equivalent to the value
of a 1913 dollar. Present this data in a graphical manner.
a. Fit both a quadratic and an exponential curve to the scatter plot of this
b. Which curve provides the best fit? Explain your reasoning, giving consideration to more than just the R values.
 Cost of Flour
In 1910, a five pound bag of flour cost $0.18; in 2011, a five pound bag of flour cost $2.75. Using the Shrinking Dollar Value Chart in , determine if the change in the price of a five pound bag of flour kept pace with the change in the value of the dollar. If it did not, determine what the 2011 price of a five pound bag of flour would be if the price had kept pace with the value of the shrinking dollar.
 Education Pays
Table 2 gives the 2010 median weekly earnings by age and education level. The entries in the Age column are approximations based on the requirement in most States that students must stay in school until
they are 16, the "normal" high school graduation age is 18, two years of
college to earn an Associate's degree, and two more for a Bachelor's degree,
then two more for a Master's degree, followed by four more years to earn a
Doctorate degree. Using the second and third columns, form a scatter plot and
then determine a trend line. Explain how you formed your trend line and give
its equation. Interpret the meaning of the slope in the context of the data.
(Source: www. Education Pays)
a. Under what conditions is the average of a consecutive set of even integers
a member of the set? Prove your result.
b. Will a person without a high school diploma be able to earn $444 a week working full time (40 hours) at minimum wage? If not what hourly wage would they need to earn?
* Supported by the National Science Foundation and the U.S. Military Academy.
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