Symmetries III

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This investigation will help you to understand how translations work and what happens when two or more translations are applied one after the other. If students are familiar with vectors, they can use them in this context to define a translation in the plane. All band ornaments have translational symmetry, and all wallpaper patterns have translational symmetry in at least two directions. Illuminations provides helpful graphics, answers, and detailed instructions for completing the activity.

Students will:

• Understand how translations work.
• Understand what happens when two or more translations are applied one after the other.

NCTM Standards and Expectations:

• Understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices.
• Use various representations to help understand the effects of simple transformations and their compositions.
• Use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as art and architecture.
• Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools.

North Carolina Curriculum Alignment