The swimming pool problem is adapted from Algebra in the K-12 Curriculum: Dilemmas and Possibilities, Final Report to the Board of Directors, by the NCTM Algebra Working Group (East Lansing. Mich.: Michigan State University 1995).
Problem and analysis of algebraic thinking discussed in "Experiences with Patterning," by Joan Ferrini-Mundy, Glenda Lappan, and Elizabeth Phillips, in Teaching Children Mathematics (February 1997), p. 282-288.
Pattern problems taken from Everyday Mathematics, Student Journal, Volume 1, Grade 3, developed by the University of Chicago Math Project (New York: SRA/McGraw-Hill, 2001).
McGraw-Hill makes no representations or warranties as to the accuracy of any information contained in the McGraw-Hill Material, including any warranties of merchantability or fitness for a particular purpose. In no event shall McGraw-Hill have any liability to any party for special, incidental, tort, or consequential damages arising out of or in connection with the McGraw-Hill Material, even if McGraw-Hill has been advised of the possibility of such damages.