Lesson 2 Workshop: Proving Symmetry
Supported route
This version makes every symmetry claim pass a physical test before learners generalise. For an investigation with fewer prompts, open the open-inquiry version of Lesson 2.
Learning target
Ākonga will distinguish reflectional symmetry from rotational symmetry and record test evidence, not a visual guess.
Prepare the test stations
Provide paper copies of six asymmetric and symmetric shapes, small mirrors, tracing paper, split pins, coloured pencils and a recording sheet with columns for claim, test and result.
Two tests, two kinds of evidence
Fold or mirror: corresponding edges must coincide across the proposed line. Trace and turn: count every matching position in one complete turn, including the final 360° return, to establish rotational order.
Evidence workshop · 60 minutes
1. Predict without committing · 6 minutes
Learners place a removable dot beside each shape they think has symmetry. They do not draw an axis or state an order until a test produces evidence.
2. Model one failed claim · 10 minutes
The teacher proposes a deliberately incorrect diagonal axis on a rectangle, tests it with a fold, and records why the claim fails. Model changing an answer when the evidence disagrees.
3. Guided station round · 20 minutes
Pairs test three shapes. Partner A operates the mirror or tracing sheet; Partner B records the outcome and names the exact line, centre or turn angle used.
Checkpoint B: each pair must show one rejected claim as well as one confirmed claim.
4. Independent verification · 14 minutes
Each learner receives a new compound shape, marks every valid mirror line, and determines its rotational order. The written reason must refer to a complete match rather than appearance.
5. Design-and-swap exit · 10 minutes
Create a grid motif with exactly two mirror lines, exchange it with a partner, and amend the design if the partner's fold test finds an extra axis or a mismatch.
Teacher checkpoint notes
If folding is difficult: supply a pre-cut shape and a bold proposed axis so the learner can focus on coincidence rather than fine-motor accuracy.
If language is the barrier: accept a photo sequence of the test with the line, centre and matching positions labelled.
Ready to progress: the learner can reject a false axis and determine a rotational order from a full-turn test without teacher prompting.
Curriculum alignment
- Te Mātaiaho (2025) · Mathematics and Statistics · Phase 4 (Years 9–10) · Geometry (Practices): “- Transforming 2D shapes in the coordinate plane by translation, reflection about a given line of symmetry, and rotation about a given point by a multiple of 90 degrees”
- NZC (2007) · Mathematics and Statistics · Level 5: “Define and use transformations and describe the invariant properties of figures and objects under these transformations.”