Lesson 4 Workshop: Reference Points and Lines
Supported route
Learners work from a reference-first checklist: mark the line or centre, transform one vertex, complete the image, then verify invariants. The open-inquiry version of Lesson 4 offers a less directed comparison of the same transformations.
Learning target
Ākonga will construct a reflection and a quarter- or half-turn rotation, naming every reference needed for another person to reproduce the result.
Reference-first checklist
Do not start with the image
For a reflection, highlight the mirror line and measure a perpendicular distance. For a rotation, circle the centre and state the angle and direction. Only then plot the first image vertex.
The final check is the same for both operations: corresponding side lengths and angles are unchanged. A correct-looking drawing without a named reference is not yet reproducible evidence.
Construction clinic · 60 minutes
1. Spot the missing reference · 7 minutes
Show three incomplete instructions. Pairs identify whether each needs a mirror line, a centre, an angle or a direction before anyone can construct the image.
2. I do: one vertex each way · 13 minutes
Model a reflection by counting perpendicular squares from the line, then model a 90° clockwise rotation with tracing paper. Narrate the checklist and mark each completed step.
3. We do: paired construction · 16 minutes
Partner A completes a reflected triangle while Partner B checks equal distances. They swap roles for a rotated quadrilateral and check equal centre-to-vertex distances.
Checkpoint D: both constructions must include primed vertex labels and an explicit reference.
4. Error clinic · 14 minutes
Learners annotate two faulty images: one measured parallel rather than perpendicular to a mirror line, and one turned about the wrong centre. They repair only the affected vertices.
5. Independent instruction card · 10 minutes
Write a complete transformation instruction for a supplied shape, trade cards, and test whether a partner can reproduce the intended image without asking a clarifying question.
Teacher checkpoint notes
For reflection support: add faint perpendicular guide segments from each original vertex to the mirror line and let the learner complete the equal distance.
For rotation support: restrict the first round to a centre at the origin and turns of 90° or 180°, with tracing paper available throughout.
Ready to progress: the learner states a complete transformation rule and verifies a constructed image using distances and invariant properties.
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.”