Students use rotations and reflections of a rectangle and other geometric shapes to study the algebraic properties of commutativity, associativity, identity, and inverse. NCTM labels this two-lesson unit for middle grades (6-8), but the ideas embodied in it (symmetry groups) are often studied in graduate level abstract algebra courses. The procedures in the lessons are carefully explained and illustrated, and ORC does not doubt that middle grades students can perform the geometric transformations and fill in the operation tables, but high school students will more likely understand the operations as elements of a mathematical system, which is the point of the unit, so ORC is recommending the lessons for grades 9-12 rather than grades 6-8. Downloadable activity sheets, discussion questions, extensions, and suggestions for assessment are included. (sw)

Arts and Communication teachers can use this two-lesson unit with career-technical students preparing to print, silk screen, or apply other graphic arts techniques. The unit's visual investigations can help develop student understanding of symmetry, rotation, and reflection, which are algebraic transformations with design applications. (jrs)