One copy of the Phase 4 planning pack per learner or pair. Pages are labelled L1–L6.
What this offering is
This is the Phase 4 teaching spine for the Hamilton Zoo mathematics family. It provides six sequenced 60-minute lessons, worked checkpoints and a printable learner pack. After this programme, learners who are ready for a denser independent investigation can continue to Hamilton Zoo Advanced Analytics — the optional interactive capstone.
Data honesty: all coordinates, visitor counts, costs and planning constraints in this programme are fictional classroom data. They are inspired by a zoo-planning context but do not describe Hamilton Zoo's real layout, operations, animals or visitor behaviour.
Cold-teach setup
Provide
Rulers, calculators, graph paper and coloured pencils. A spreadsheet or graphing tool is optional, never required.
Group
Use pairs for checking calculations, then require each learner to annotate the evidence they personally understand.
Protect
Assess mathematics, not prior zoo knowledge, drawing polish, device access or public-speaking confidence.
Six-lesson learning arc
| Lesson | Mathematical move | Evidence produced |
|---|---|---|
| 1. Coordinate brief | Read and construct a four-quadrant planning model. | Scale, origin, plotted sites and two checked coordinates. |
| 2. Distance routes | Derive and use the distance formula through right triangles. | Three distances, units and a justified route choice. |
| 3. Transformations | Translate, reflect and rotate footprints by multiples of 90°. | New vertices plus an invariant check. |
| 4. Linear models | Interpret gradient and intercept in a synthetic visitor-flow model. | Graph, equation, prediction and limitation statement. |
| 5. Constraint testing | Calculate perimeter and area, then compare feasible design options. | Decision matrix with calculations and trade-offs. |
| 6. Expansion proposal | Select and combine evidence without hiding assumptions. | One-page proposal and a calculation audit trail. |
🎯 Curriculum Links | Te Hononga ki te Marautanga
Exact Phase 4 curriculum anchors
The lessons teach these active Mathematics and Statistics statements directly. The quotations below are byte-faithful to the live curriculum corpus.
- Using Pythagoras’ theorem to:find the length of an unknown side in a right-angled trianglecheck if a triangle has a right anglecalculate the distance between two points in the coordinate plane, yielding the distance formula d = √(x2 − x1)2 + (y2 − y1)2 - find the length of an unknown side in a right-angled triangle - check if a triangle has a right angle - calculate the distance between two points in the coordinate plane, yielding the distance formula d = √(x2 − x1)2 + (y2 − y1)2
- 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
- Interpreting and graphing linear equations in the form y = mx + c, using the gradient and y-intercept - Calculating the gradient and y-intercept of a line, using a graph - Comparing the relative magnitude of m in two or more linear graphs, using the concept of steepness and relating it to the magnitude of m - Finding the equation of a line, given two points or the gradient and a single point - Determining the effect on graphs in the coordinate plane of changing the coefficient of x2 and the fixed value c, for a range of quadratic equations of the form y = ax2 or y = x2 + c, where a is a positive integer and c is an integer
- Finding:the perimeter of 2D shapesthe circumference of circlesthe area of parallelograms, trapeziums, and kites, relating the formulae used to the formula for a rectangle - the perimeter of 2D shapes - the circumference of circles - the area of parallelograms, trapeziums, and kites, relating the formulae used to the formula for a rectangle - Deriving the formulae for the perimeter of half and quarter circles from the formula for a full circle - Calculating the perimeter of half circles and quarter circles
Te Whare Ako | Why these teaching moves
The sequence uses worked modelling, peer checking and visible success evidence so errors become discussable before the capstone. See Assessment for Learning for feedback and evidence design, and Universal Design for Learning for multiple ways to access and communicate mathematical reasoning.
Assessment contract
The final proposal is sufficient when it includes:
- a labelled coordinate model with scale and units;
- two accurate distance calculations and one checked transformation;
- one linear model interpreted in the planning context;
- a feasible option selected against stated constraints;
- one limitation explaining what the synthetic model cannot prove.
Choice-preserving evidence: learners may submit a written, diagram-led, recorded or teacher-conferenced explanation. Mathematical reasoning is the assessed evidence; presentation performance and personal disclosure are not.