Ohio Resource Center
Lessons
Algebraic Transformations
Discipline
Mathematics
7, 8, 9
Professional Commentary

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 older students will more likely understand the operations as elements of a mathematical system, which is the point of the unit. Downloadable activity sheets, discussion questions, extensions, suggestions for assessment, and prompts for teacher reflection are included. (sw)

Common Core State Standards for Mathematics
Geometry
Understand congruence and similarity using physical models, transparencies, or geometry software.
8.G.A.1
Verify experimentally the properties of rotations, reflections, and translations:
1. Lines are taken to lines, and line segments to line segments of the same length.
2. Angles are taken to angles of the same measure.
3. Parallel lines are taken to parallel lines.
Ohio Mathematics Academic Content Standards (2001)
Geometry and Spatial Sense Standard