Ohio Resource Center
Content Supports
Symmetries III
Discipline
Mathematics
6, 7, 8, 9, 10, 11, 12
Professional Commentary

Take a shape, move it from here to there, and that's a translation. Translations are the simplest of the symmetry transformations and they are also the most important. Artists use translations to create band ornaments and wallpaper patterns. In this investigation using a JavaSketchpad applet, students learn the mathematical definitions and properties of translations and translation symmetry. Ideas from Part 1 and Part 2 on rotation and reflection symmetry are incorporated in the discussion questions. Answers to the proposed activities are provided. (author/sw)

Ohio Mathematics Academic Content Standards (2001)
Geometry and Spatial Sense Standard
Benchmarks (5–7)
F.
Describe and use the concepts of congruence, similarity and symmetry to solve problems.
H.
Predict and describe results (size, position, orientation) of transformations of two-dimensional figures.
Benchmarks (8–10)
F.
Represent and model transformations in a coordinate plane and describe the results.
H.
Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.
5.
Predict and describe sizes, positions and orientations of two-dimensional shapes after transformations such as reflections, rotations, translations and dilations.
8.
Perform translations, reflections, rotations and dilations of two-dimensional figures using a variety of methods (paper folding, tracing, graph paper).
1.
Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects.
5.
Draw the results of translations, reflections, rotations and dilations of objects in the coordinate plane, and determine properties that remain fixed; e.g., lengths of sides remain the same under translations.