Lesson 6 Workshop: Supported Design Synthesis
Supported route
This evidence task divides design, construction and explanation into teacher-checkable stages. The open-inquiry version of Lesson 6 is better suited to learners who can manage a less structured design brief.
Outcome
Ākonga produce an original neutral geometric border or tile, apply two named transformations, and submit annotated evidence that another learner could use to reproduce the pattern.
Design boundaries
Use a self-created geometric motif unless the teacher has supplied an image approved for this learning context. Do not copy a cultural design or invent its meaning from its geometry.
- The base motif fits inside a labelled grid cell.
- At least four images of that motif are visible.
- Two transformation rules name every required reference.
- Corresponding lengths and angles have been checked.
Checkpoint pathway · 1–2 lessons
Checkpoint 1: approve the plan
Submit a thumbnail showing the base motif, the intended repeat direction, and two proposed transformations. The teacher checks that each rule is possible before construction begins.
Checkpoint 2: construct one repeat
Complete the first transformed image and overlay it with tracing paper where appropriate. Repair any changed length, angle or orientation that is not required by the stated rule.
Checkpoint 3: extend and peer-test
Extend the design to at least four images. A partner follows the written rules on a blank grid and marks any instruction that lacks a line, centre, angle, direction or distance.
Checkpoint 4: attach mathematical evidence
Label the original motif and two images, draw the transformation references, and write a short explanation connecting each visible result to its rule and invariant check.
Teacher conference guide
| Evidence focus | Prompt when support is needed | Observable completion |
|---|---|---|
| Rule | Which line, centre, angle, direction or distance is missing? | A peer can reproduce both transformations from the labels alone. |
| Accuracy | Which corresponding measurement should remain unchanged? | Motif images are congruent and match the stated orientations. |
| Reasoning | What visible feature proves this is the transformation you named? | The explanation cites a rule, a reference and an invariant check. |
Access and pacing notes
Minimum supported product: one motif, four images, one translation and one reflection or rotation, all on a teacher-supplied grid.
Oral-first option: record the explanation in a teacher conference, then use the recording to produce labels or a short written paragraph.
Completion evidence: keep the planning thumbnail, the peer-tested rule card and the final annotated design together so progress is visible as well as the polished result.
Curriculum alignment
- Te Mātaiaho (2025) · Mathematics and Statistics · Phase 4 (Years 9–10) · Geometry (Knowledge): “- A set of points in a plane can be transformed by translation, reflection about a line, and rotation about a fixed point.”
- 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.”