Correction: Problem Solving: Tips For TeachersSource: The Arithmetic Teacher, Vol. 33, No. 4 (December 1985), p. 48Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/80000190 .

Accessed: 12/06/2014 12:44

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact support@jstor.org.

.

National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extendaccess to The Arithmetic Teacher.

http://www.jstor.org

This content downloaded from 91.229.229.44 on Thu, 12 Jun 2014 12:44:30 PMAll use subject to JSTOR Terms and Conditions

Reader*1 DICltOQIK!

[Continued from page 26)

The crossword answer space shown here is not complete. Only some of the blackened squares are provided. Using the information in the previous paragraph, locate the rest of the squares.

Answer:

William D. Ja m ski Indiana University òoutheast New Albany, IN 47150

Insights into density

In the discussion of the density property of the rational numbers with preservice elemen- tary teachers, I usually ask, "Can you find a rational number midway between two rational numbers?" We then discuss the averaging method, along with the fact that it is always possible to find a rational number between any two rational numbers.

In my last discussion, a student spoke up, "I've found another way to get a rational number between two rational numbers. I just add the numerators to find the new numerator and add the denominators to get the new de- nominator." The question from the class was, "Does it always work?" Examples were test- ed by using the fact that if alb < eld where a, b, c, and d are integers and b and d are posi

tive, then ad < be. We ended up writing a proof as follows:

If a, b, с and d are integers and b and d are positive and alb < eld, then ad < be.

If we assume that

a a + с ~b< b + ď

then we know that

a (b + a) < b(a + c), or

ab + ad < ab + be.

Subtracting ab from each side of the inequal- ity results in ad < be, which was given.

Similarly, if we assume that

a + с с d + d </

then

or (α + c)d < e(b + d),

ad + cd < be + cd.

Subtracting cd from each side of the inequality yields ad < be, which was given. A review of the reasoning in these steps yields

a a + с с

~b K

b + d <

~d'

The class experience was valuable not only because students applied previous knowledge in a new exploration but also because they learned that they could "discover" some mathematics not in their textbook.

M. Geralda Schaefer ran American University Edinburg, TX 78539

Correction

In the "Problem Corner" in "Problem Solv- ing: Tips for Teachers" in the September 1985 issue (p. 39), the answer should be 246. (Lucien T. Hall, Richmond, Virginia; Jean E. Hershner, Arnold, Maryland; Kathleen Brima- combe, Stone Mountain, Georgia; K. Deborah Boutier, Arlington, Texas)

t NCTM ORDER FORM___ Educational Materials · Stock* · Quantity · Unit Price · Total Price

$ $ $ $ $ $ 20% Discount: Individual members, bookstores, or quantity orders for 10 or more SUBTOTAL $ copies of a single title shipped to one address. Prices subject to change without notice. Virginia residents add 4% sales tax. Billed orders will include shipping Less 20% $ and handling charges.

MEMBERSHIP dues support the development, coordination and delivery of NCTM services, including $13 for each ARITHMETIC TEACHER and MATHEMATICS TEACHER subscription and $2 for five issues of the NCTM News Bulletin.

U Arithmetic Teacher (AT) · 9 issues, September-May, for elementary school teachers, parents, and teacher educators. Individuals $35; Institutions $40* * Additional AT copies for institutions mailed to the same address $13/0RDER/YEAR. $

G Mathematics Teacher (MT) · 9 issues, September-May, for secondary school and two-year college mathematics teachers, and teacher educators. Individuals $35; Institutions $40. $

D Both Arithmetic Teacher and Mathematics Teacher for individuals only $48. $ Full-time student dues are Vfe regular membership dues. For mailing outside the U.S., add $5 for the first AT or MT per membership and $2.50 for each additional AT or MT

TOTAL $ Member # , D Payment to NCTM in U.S. funds endosed.

Name D MasterCwi D VISA Expires

Address __ Credit Card #

City State or ZIPor Signature Province Poetai Code 585A1

^нш1906 Association Drtv· · Boston, VA 22091 · (703) 620-0840™^

48 Arithmetic Teacher

This content downloaded from 91.229.229.44 on Thu, 12 Jun 2014 12:44:30 PMAll use subject to JSTOR Terms and Conditions