On Day 3, we did two different sets of activities:

- We revisited the definition of a group and its properties in the context of cyclic groups, namely C
_{1}, C_{2}, C_{3}, C_{4}, and C_{6},_{ }encoding the rotational symmetry of polygons we played with on Day 2. Particular features of the cyclic groups prompted a natural introduction to a few new concepts and new terminology:*Order of a group**Order of an element of a group*- Group
*generators* - Group multiplication (Cayley) table, which students worked out for C
_{3}, C_{4}, and C_{6}.

- We began exploring the symmetries of a rectangle, but this time including the reflections. This allowed us study the above-listed concepts in a different context and practice carrying out group multiplication and finding inverses.

The plan was to use 2 to segue into dihedral groups, but it seems more pedagogical to spend another class or two on exploring the cyclic groups in more depth.