# Year 5 Frieze Patterns

Australian curriculum number (ACMMG114)

## Who is this Sequence for?

Students beginning this sequence will have had prior experience of transforming shapes by flipping, reflecting in a mirror or rotating them. They will understand the concept of symmetry, and will be able to identify the line of symmetry in a shape such as a butterfly. At a simple level, these lessons provide substantial manipulative experience of geometric transformations, but they may also provide substantial challenges requiring strong visualisation and careful geometric analysis.

## Summary of learning goals

This sequence of three lessons is an exploration of symmetry and transformation in the context of friezes (repeating strip patterns). Friezes are widely used as decorative borders on furnishings, furniture, fabrics and architecture. They are seen in fencing and railings, and even on tyre treads. 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.

## Rationale for this sequence

The first lesson introduces the symmetries with simple footprints designs, and the second lesson re-examines these ideas with more complex design elements. In the third lesson students create their own friezes with desired symmetries, following a procedure described with the language of transformations that they have learned. A confident understanding of the effect of these transformations is thereby built up over the sequence.

The sequence begins the work on transformations with students analysing how to make patterns from footprints, giving a physical meaning to rotation (turn or spin), translation (step or jump) and reflection (swapping left and right feet).  The work then moves to designs on paper, with manipulation of overlays and possible use of mirrors providing assistance to build visualisation of the effect of transformations and different types of symmetry.  Some students will be easily able to visualise a transformed image after these experiences; all students will know what to use to help them find it. Students’ fluency with these transformations and symmetry is developed across the lesson sequence.

Throughout this sequence, a wide range of examples of friezes are encountered, from footprints in the sand, to the furnishings of Parliament House, wrought iron lace on terrace houses, and then tyre treads. In addition, students are encouraged to find friezes in their own environments and bring sketches or pictures to the class display.

### reSolve Mathematics is Purposeful

Geometry is all around us, and these lessons on the symmetries in friezes provide multiple opportunities for students to observe how geometry is evident in the world around us. Geometry also has close links to art and this sequence provides opportunities for demonstrating both mathematical and artistic creativity.

Whereas in earlier years, geometry in the environment is about the shapes that can be seen, this sequence moves on to highlight the mathematical relationships between shapes that make up the pattern.

Students’ fluency with transformations is developed as they classify patterns and create their own frieze designs.

### reSolve Tasks are Challenging Yet Accessible

Access is provided for all students by beginning to study transformations related to simple physical movements (footprints patterns) and by providing manipulable transparent overlays (and possibly mirrors) to support visualisation.

The types of symmetries of friezes vary in complexity, so while some students may focus on patterns with basic symmetry, students who require further challenge are extended through complex movements and complex designs. The opportunity to create their own frieze patterns allows students to engage in the activity at a variety of levels of complexity.

The attractive designs involved should appeal to students with a range of interests relating to art and design. Several of the world’s cultures are known for their frieze designs.

### reSolve Classrooms Have a Knowledge Building Culture

Students work collaboratively to sort and classify the frieze patterns. In their small groups and/or pairs, students are encouraged to build consensus on the symmetry of designs through active exploration, mathematical reasoning and clear communication.