L1 · Name:________________________Date:____________

Coordinate brief

Data note: this is a fictional classroom planning model. It is not a map of Hamilton Zoo.

Model contract: origin O(0,0) is the fictional visitor hub; 1 coordinate unit = 10 m.

Site Coordinate Quadrant or axis
Gate G (−10,−6)
Habitat H (−6,5)
Wetland W (4,8)
Clinic C (8,−4)
Hub O (0,0)
Rest area R₁ (−2,7)
Rest area R₂ (6,2)

Construct

Draw axes from −12 to 12, label scale and units, then plot all seven sites.

Peer check: cover the table. Ask a partner to recover H and C from your model.

H = ________   C = ________   Partner initials: ________
L2 · Name:________________________Date:____________

Distance and route evidence

Use d = √[(x₂−x₁)²+(y₂−y₁)²]. Keep exact values until the final step; then round to one decimal place and convert using 1 unit = 10 m.

Route Δx Δy Substitution Distance (m)
O→W
O→C
O→H
O→R₂
R₂→W
Decision: the fictional direct O→W path is restricted. Does the O→R₂→W detour stay below 130 m? Show enough evidence for another learner to audit.

The shortest route is not automatically the selected route because:

L3 · Name:________________________Date:____________

Transformation test

Original rectangle: A(−4,1), B(0,1), C(0,4), D(−4,4).

Move A′ B′ C′ D′ Invariant check
Translate by (3,−5)
Reflect in y-axis
Rotate 90° anticlockwise about origin

Falsify one result

Choose one transformed footprint. Check every vertex using the stated rule, then verify one invariant such as side length, angle or area.

Mathematics can show the new location and shape, but it cannot decide real-world suitability because:

L4 · Name:________________________Date:____________

Linear models and limits

All visitor counts below are synthetic classroom data.

Let t be hours after 9:00 am. Let V be the modelled number of visitors passing a fictional checkpoint during that hour.

t 0 1 2 3 4
Model A: V 40 75 110 145 180

Constant difference: ________   Equation: ____________________   Gradient meaning: ______________________________

Model B: V=25t+70. Find when both models give the same prediction.

Graph and limitation

A prediction from this model becomes unreliable when:

L5 · Name:________________________Date:____________

Constraint decision

Hard constraints: area ≥1,000 m²; perimeter ≤150 m; centre route <110 m; barrier cost ≤$90,000 at $600 per metre in this fictional scenario.

Option Dimensions Centre route
A Rectangle 40 m × 30 m 80 m
B Rectangle 50 m × 22 m 95 m
C Parallelogram: base 45 m, perpendicular height 25 m, side 28 m 105 m
D Rectangle 60 m × 18 m 100 m
E Rectangle 35 m × 30 m 115 m
Option Area Perimeter Cost All constraints pass?
A
B
C
D
E

Reject before you prefer: which options fail, and on which constraint? ______________________________________________________

My declared preference after feasibility: __________________________________________

Recommended option and mathematical reason:

Trade-off or missing evidence:

L6 · Name:________________________Date:____________

Auditable expansion proposal

Required honesty: identify the data as synthetic. Your model cannot determine actual animal welfare, engineering feasibility, visitor behaviour or Hamilton Zoo decisions.

Recommendation

Evidence checklist

☐ Labelled coordinate model with scale and units ☐ Two checked distance calculations
☐ One transformation with invariant check ☐ Linear model with gradient and intercept interpreted
☐ Constraint matrix and declared preference ☐ One assumption and one limitation

Calculation audit trail

Claim → evidence → reasoning

Peer auditor: reproduce one calculation without asking the author. Calculation checked: __________________ Result agrees? Yes / Repair needed

Limitation: