Vision - Potential
Vision Within Every Instructor - Potential Within Every Student
Newsletter of the HBCU College Algebra Reform Consortium*
Number 109, February 2012
www.ContemporaryCollegeAlgebra.org

Contents:
[1] PREP 2012 [2] Fun Project: Pascal's Triangle [3] Shrinking Value of the Dollar [4] Cost of Flour [5] Education Pays [6] Queries [7] Notices

[1] 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

Bloomington, MN

2. Improving College Mathematics

Teaching Through Faculty

Development

Gerald Kobyiski, Hilary Fletcher,

Tina Hartly

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

Lincoln, NE

4. Using Inquiry Based Learning in

Second-Year Calculus For

Perspective Teachers

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

Under-graduate Calculus

Daniel Kaplan, Randall Pruim,

Eric Markland, Nicholas Horton

July 9-13, 2012

Grand Rapids, MI

7. Teaching That Emphasizes

Mathematical Practices for

K-8 Teachers

Phyllis Chinn and Dale Oliver

July 15-20, 2012

Arcata, CA

8. Beyond Introductory Statistics:

Generalized Linear and

Multilevel Models

Jim Albert and Brad Hartlaub

July 16-20, 2012

Gambier, OH

9. (Online) Sage: Using Open-Source

Mathematics Software with

Undergraduates

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.

[2] 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 0.

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 upper right.

Some activities to be explored in developing a small group, Fun Project on Pascal's Triangle:

1. Construct the row of Pascal's Triangle.

2. Show that the entries in the third row are the coefficients in the expansion of .

3. Show that the sum of the entries in the row is

4. Illustrate and then explain why the number of combinations of things taken at a time, , is the entry in the row and k column.

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 tetrahedral numbers.

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).

[3] 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.

Year	Amount =	Year	Amount =
	$1 in 1913		$1 in 1913
1913	$1	1970	$3.92
1920	$2.02	1975	$5.43
1925	$1.77	1980	$8.32
1930	$1.69	1985	$10.87
1935	$1.38	1990	$13.20
1940	$1.41	1995	$15.39
1945	$1.82	2000	$17.39
1950	$2.43	2005	$19.73
1955	$2.71	2008	$21.57
1960	$2.99	2011	$22.73
1965	$3.18

Table 1

a. Fit both a quadratic and an exponential curve to the scatter plot of this data.

b. Which curve provides the best fit? Explain your reasoning, giving consideration to more than just the R values.

[4] 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 [2], 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.

[5] 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)

Educational	Age	Median Weekly
Level		Earnings
Less than H.S.	16	$444
H.S. Diploma	18	$626
Assoc. Degree	20	$767
Bachelor Degree	22	$1,038
Master Degree	24	$1,272
Doctorate Degree	28	$1,550

Table 2

[6] Queries

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?

[7] Notices

1. Phil Rudder is the McGraw-Hill Representative for Contemporary College Algebra: Data, Functions, Modeling. 563.584.6323, [phil_rudder@mcgraw-hill.com]

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* Supported by the National Science Foundation and the U.S. Military Academy.