- Introduce the transformations reflection, translation, rotation and (optionally) glide reflection.
- (Optional) Identify the symmetries of an object.
- Interest visual, artistic, and kinesthetic learners in the topic of transformations and symmetry.
- Assess students' understanding of the concepts introduced.

For examples of the types of symmetry to be demonstrated, see The Four Types of Symmetry in the Plane on the Math Forum web site.

**Description of Activity**

Have students work in pairs. This will reduce the demand for manipulatives and allow students to reinforce each others' knowledge. Smaller groups are more desirable than larger ones because of the simplicity of the task and the goal of assessing each students' understanding.

Distribute manipulatives to students; you may use pattern blocks or any manipulative that can easily be arranged into a repeatable design.

Have students create a "motif" -- a design they will be reproducing. Warn them that the design should be relatively simple because they will need to reproduce it.

Demonstrate a translation for the class by using your own motif and a transformed copy of the motif. Ask each pair to create a translated copy of their motif. As they work, watch their efforts: this should be relatively easy for all students.

Demonstrate a reflection for the class in the same way and ask them to create reflected images of their motifs. Students may need some help in reversing their design. It is likely that some pair of students will be able to provide an example of a reflection of a motif with mirror symmetry; remark to the class on how the motif looks the same after reflection as before.

Demonstrate a rotation for the class; indicate the center point of the rotation using a dime or other small marker. Demonstrate rotations through several different angles. Ask the class to construct copies of their motifs that are rotated through a 180 degree angle; as you review their work, ask them to show you the center of rotation. (Students who finish early can be asked to construct rotations through different angles.) You may also wish to ask students what happens if their motif is rotated about its own center, informally introducing the concept of rotational symmetry of an object.

Depending on the ability level of the class, the time remaining, and the frustration level of your students you may or may not wish to introduce glide reflections.

**Directions for Further Exploration**

- Create symmetric patterns using these transformations.
- Demonstrate the transformation tools provided with The Geometer's Sketchpad software.
- Formally introduce the concept of symmetry of a design or motif.
- Identify symmetries in a pattern. (Note: glide symmetries are often difficult to detect.)