Cycling with the Primes

This resource consists of 5 worksheets and a 6 page Teacher’s Guide. These worksheets explore the amazing symmetries occurring in the decimal expansions of prime reciprocals. Students investigate the cycles of digits in these expansions and complete beautiful cyclic diagrams, templates of which are supplied in these worksheets. The primes 3, 7, 13, 17, 19, 23, 29, 31 and 37 are explored. Hidden patterns are revealed and a connection between the number of cycles and the length of the cycles is discovered.
The completed diagrams are given in the Teacher’s Guide which also contains the outline of an investigative approach to the topic. Details are given of the various stages of the investigation and how the worksheets may be incorporated. Various extensions are suggested including the use of a spreadsheet.
This is a fascinating topic which will provide rich and rewarding mathematical experiences for the students.