South Pacific Journey

These activities investigate reflectional and translation symmetry. Students at this level should be very familiar with the ideas of reflectional and translation symmetry. Any students having difficulty identifying reflectional symmetry in Activity One may find it useful to put a mirror on the pattern and then move the mirror down the pattern until the reflection in the mirror is the same as the pattern behind the mirror. They continue moving down the pattern to identify any other lines of reflectional symmetry and then repeat this procedure with the mirror moving across the pattern.
It is important to point out to the students that while these examples of Pacific art appear symmetrical, the symmetry is not rigid. Most patterns from Pacific art are hand drawn and rigidly straight lines are rare. If the students draw the patterns for Activities Two and Three freehand rather than using a ruler or a compass, they will get a better likeness to the original designs. You may also need to point out that the dotted lines in Activity Two are lines of reflectional symmetry.
A langanga is the unit of measurement in a Tongan ngatu. While the length of a langanga (often based on the span of a hand) may vary between ngatu, the length will always be the same within each ngatu.
Page 13 of Geometry, Figure It Out, Levels 2–3 also looks at reflectional symmetry and asks students to complete patterns.

Answers to Activities

Activity One

1. Yes, patterns b, c and d.
2a. No lines of symmetry.

Activity Two

Activity Three

1.

2. 10m