Ohio Resource Center
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Lessons
Algebraic Transformations
Discipline
Mathematics
Grades
7, 8, 9
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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
Grade 8
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
Grade Level Indicators (Grade 10)
9.
Show and describe the results of combinations of translations, reflections and rotations (compositions); e.g., perform compositions and specify the result of a composition as the outcome of a single motion, when applicable.
Principles and Standards for School Mathematics
Geometry Standard
Apply transformations and use symmetry to analyze mathematical situations
Expectations (9–12)
use various representations to help understand the effects of simple transformations and their compositions.
Use visualization, spatial reasoning, and geometric modeling to solve problems
Expectations (9–12)
use various representations to help understand the effects of simple transformations and their compositions.
use geometric models to gain insights into, and answer questions in, other areas of mathematics;