REFLECTING WITH ONE MIRROR & DIHEDRAL SYMMETRY

Objective:

Students will understand properties of reflection and symmetry using one mirror.

flat edged mirrors, reflective on both sides (obtained by taping two regular mirrors back to back)
protractors
Reflecting with One Mirror Activity Sheet

With a full length mirror and a student volunteer pose questions about mirror reflections. For example:
• What happens to the image as the student moves left hand?
  
• What happens to the image as the mirror is tipped at different angles?
  
• Where is the image located relative to the student?
  
• What are some relationships between a figure and its mirror image?
  

DO NOT apply your marker directly to the screen. We suggest printing a hardcopy of the activity sheet directly from your browser to work on.
• This lesson is divided into three independent sections to allow for teacher flexibility.
  
• At the end of each section have the class discuss their conclusions.
  

Make sure that the following points are brought out during the discussions:

Objects are reversed under reflections. A good example of this is the word 'ambulance' written reversed on the front of ambulances allowing drivers to read it in their mirrors.

• A figure which has dihedral symmetry has both reflective and rotational symmetry.

• Dihedral symmetry is different from reflective symmetry because in reflective symmetry the lines of reflections do not necessarily intersect to form equal angles. (i.e., parallel mirrors are not dihedral)

• Dihedral symmetry is different from rotational symmetry because rotational symmetry may not have lines of reflection.

This section is intended to start the students thinking about angles of reflection. Do not worry about the 'correctness' of the students' ideas at this point, as they continue through the KaleidoTile unit they will be forming their own conclusions about mirror and image angle relationships.

Discuss other types of symmetry such as rotation and translation and where they may occur in the world. These transformations will be addressed further in Lesson 4: Reflecting with Two Mirrors & Dihedral Symmetry.