# Transformations: Frieze Patterns

Australian curriculum number (ACMMG181)

Using the formal terminology of transformations (reflection, translation and rotation), students explore the effects of transformations on friezes and identify and describe line symmetry and rotational symmetry (including the centre of rotation and axes of symmetry). Students move beyond looking at examples of symmetry to using symmetry as a way to classify designs, thereby building up a more abstract notion of pattern in mathematics.

This sequence is for students who:

• have had prior experience of transforming shapes by flipping, reflecting or rotating them.
• are familiar with the formal language of transformations (reflection, rotation and translation).
• understand the concept of symmetry and can identify the line of symmetry in a shape.

### Lesson 1: Footprints in the Sand

Students physically recreate the movements used to make patterns of footprints left in sand. They revisit the ideas of flip, slide, turn, and mirror image and symmetry (of earlier years), as well as the more precise language of reflections, rotations and translations. They explore symmetries in the footprint patterns.

### Lesson 2: Frieze Patterns

This task introduces friezes with examples from decor in Old Parliament House, Canberra. Students identify the different symmetries that are present in frieze patterns and then group the patterns based on their symmetries. They consolidate their learning by looking at what would happen if one panel in a wrought iron lace railing was installed the wrong way around.

### Lesson 3: Creating Frieze Patterns

Students create their own frieze designs with chosen symmetries. First, they create a cell by applying transformations to a design element. This cell is then repeatedly translated a fixed distance to create a frieze. Together, students make a class display of friezes.

Last updated June 20 2020.