Transformations

Class: Geometry 10th grade

Unit:  Transformations

Objectives

• The students will be able to recognize reflection and rotation symmetry.
• The students will be able to create cyclic and dihedral figures using Geometer’s Sketchpad.

Standards (NCTM- Geometry)

• Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools.
• Use various representations to help understand the effects of simple transformations and their compositions.
• Understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices.

Anticipatory Set

Show a picture of the old and new frieze pattern at Yankee Stadium, as well as other pictures of symmetry from other sports stadiums.

Teaching:  Input

• Introduce symmetry, by asking what the students already know (KWL).  We will develop a definition.
• I will give each student an equilateral triangle and ask them to draw lines of symmetry, rotate it so it ends up in the same position, and talk about other objects in life and nature that have symmetries.

Teaching: Modeling

• The students will take out the activity sheet, which has pictures of various shapes that have reflection symmetry.
• We will talk about vertical and horizontal symmetry, and rotational symmetry.
• The students will come to the Smart board and be able to create images of shapes that have these types of symmetry.  They will also be able to rotate them with their fingers using Geometer’s Sketchpad.

Teaching:  Checking for Understanding

• The students will be answering questions and discussing while I will be checking to make sure they are on task and knowing what we are talking about.
• The students will also be at computers or at the Smart board creating their own images that have types of symmetry using Geometer’s Sketchpad, so I will be watching to make sure they understand the objectives.

Guided Practice

• There is a guided practice worksheet that will be handed out.  The worksheet includes some notes, as well as pictures and questions.

Closure

• I will be summarizing what we have learned for the students and reinforcing the types of horizontal, vertical, and rotational symmetry, and mentioning the frieze at Yankee Stadium again.

Independent Practice

• I will be assigning a two-page worksheet for homework and an extra (possibly voluntary) project about creating a tessellation.  Many of the students do this at some point in art class and are familiar with them.

Materials 

• Symmetry Activity Sheet
• Paper cut of equilateral triangle
• Protractor and straight edge
• Smart board with Internet access, and Geometer’s sketchpad.

Duration:  1 – 40 minute class period