Lesson 6: Defend the proposal

Select the strongest mathematical evidence, expose assumptions and submit a proposal another learner can audit.

Learning intention and success evidence

We are learning to synthesise mathematical representations into an auditable recommendation.

Curriculum synthesis

This capstone integrates the exact Phase 4 anchors taught in Lessons 2–5: coordinate-plane distance (47313), transformations (18236), linear equations and gradient (47493), and perimeter/area (47304). No new curriculum alignment is inferred from the act of presenting.

Preparation

Print: learner pack page L6 or provide one A3 sheet. Return each learner's checked work from Lessons 1–5. Choose whether the final explanation will be written, diagram-led, recorded or a teacher conference; all modes use the same evidence criteria.

60-minute runsheet

  1. Whakaoho — evidence triage (5 min): classify sample statements as calculation, interpretation, assumption or limitation.
  2. Exemplar deconstruction (10 min): model a small claim-evidence-reasoning paragraph: “Choose Option A” → 1,200 m², 140 m perimeter, $84,000 cost in the fictional scenario → all constraints pass and it has the lowest cost among the feasible options.
  3. Proposal build (25 min): learners assemble the required coordinate model, two distances, one checked transformation, one interpreted linear model and the constraint decision.
  4. Audit exchange (12 min): a partner chooses one calculation and reproduces it without help. The author repairs any missing values, units or assumptions.
  5. Limitation and revision (5 min): learners add one honest boundary: the synthetic mathematics does not determine animal welfare, engineering feasibility, actual visitor behaviour or Hamilton Zoo decisions.
  6. Submit (3 min): highlight the recommendation, box the strongest calculation and underline the limitation.

Assessment guide

Evidence Secure Needs repair
Coordinate model Origin, scale, units and positions are recoverable. Axes or scale are ambiguous.
Calculations Methods, substitutions, results and units can be checked. Answers appear without an audit trail.
Interpretation Gradient, distance or transformation is explained in context. Symbols are named but not interpreted.
Decision Feasibility is separated from preference. “Best” is asserted without constraints.
Honesty At least one assumption and limitation are explicit. Synthetic data is presented as real zoo evidence.

Next pathway

Learners who meet the secure evidence contract can continue to the advanced interactive investigation. It is an optional capstone, not a replacement for this six-lesson teaching sequence.