Discovering the regularity by pupils is the important problem and present inthe world trends of teaching. In many countries in the teaching of mathematicsthe attention is directed to the functioning of the regularity. In literature onecan find descriptions of carried out research in discovering and generalizing ofnoticed rules (Stacey, 1989; Mason, 1996; Lee, 1996; Garc´ıa Cruz, Martinón,1997; Sasman, Olivier, Linchevski, 1999; Orton, A., Orton, J., 1999; Zazkis, Liljedahl,2002a, 2002b; Littler, Benson, 2005a, 2005b; Barbosa, Palhares, Vale,2007; Carraher, Martinez, Schliemann, 2008)
