In what follows, I will share with you several Escher-based activities that I use with middle school children (grades 5 to 8) to promote mathematics as the study of patterns. All exercise sheets will be found in the book Investigating Patterns: Symmetry and Tessellations. The activities in this book have been coordinated with appropriate Internet Links for teacher and student use.
A methodical analysis of Escher's tessellations requires a familiarity with the kinds of symmetry they exhibit. To begin, students are exposed to reflectional symmetry and rotational symmetry through a set of exercises involving animals and insects, letters of the alphabet, national flags, and familiar logos.

reflectional symmetry

rotational symmetry
The trail left by a biped hopping on one foot has translational symmetry. The one left by a biped with a human gait has glide-reflectional symmetry. Exercises involving symmetrical strip patterns (frieze patterns) are used to reinforce these ideas.

translational symmetry

glide-reflectional symmetry