Checked 29 September 2026. The official QCAA Specialist Mathematics 2025 v1.4 syllabus gives Unit 1 Topic 1 two subtopics: 4-hour introduction to counting techniques and 8-hour permutations/combinations (printed pp 16–17). This 250-minute timetable-shaped opener develops only the first subtopic. It is 10 minutes beyond the notional four hours and leaves the 8-hour subtopic plus the rest of the 55-hour unit to the school. The maths examples and contexts are invented; no empirical survey data is claimed.
Seat 1 · teacher with five minutes to start
Open Day 1, A and the two-set map. Place five shared-name tokens in the overlap first, then 12 and 8 in the exclusive regions, and five outside. The learner can see why 17+13−5=25; a teacher has the exit answer and a worked swap ready. On Days 5/10 use fresh G/H/I and withhold the public key until the first response. Neutral reading and tactile placement are access support; saying which formula to use is a content hint. A real class may need more than the seven-minute independent window; extend time rather than turning speed into a mathematical score.
Seat 2 · learner's route followed by hand
For Day 3 C: add set totals 12+11+9=32; subtract inclusive pair counts 4+3+5=12; add the two all-three people back, giving 22. Build disjoint regions: A only 7, R only 4, C only 3, AR only 2, AC only 1, RC only 3, all three 2. They sum 22; with universe 28, six choose none. A spoken explanation, a labelled graphic or raised cards must make the same pairwise-inclusive assumption. Reading or handwriting ability is considered separately from counting reasoning. If a pair count were smaller than the centre, the data would be impossible; this is a useful self-check.
For fresh G, independent calculation gives 27 in at least one station, 9 neither and 5 one-session bookings. For H, three-set inclusion–exclusion gives 28 in at least one, 8 in none; seven nonnegative regions rebuild all set/pair totals. I gives 3×2 + 2×3 = 12 complete routes. The separate teacher key states what a wrong product would count, so feedback can target the model rather than just marking a number wrong. The verifier independently recomputes these with integer set/branch enumerations.
Seat 3 · assessor or potential funder
Defensible output: ten distinct 25-minute scripts, 30 same-target routes, 20 worked optional swaps, 20 application bridges, two fresh public formative checks and a separate worked key, six original searchable A4 SVG/PDF aids with exact text/tactile equivalents. The syllabus version, subtopic hours and scope boundary are explicit. The aids and cases are CC BY 4.0 authored work; QCAA material is cited, not republished. There is no measured classroom uptake, learning gain, controlled accessibility study, independent maths educator review, QCAA endorsement, translation validation or complete Unit 1 coverage. The checks cannot be secure school instruments while their key is public.
Mechanical and visual review boundary
python3 verify_pack.py checks the version/scope markers, ten timed scripts, 30 routes, 20 worked swaps, fresh-file isolation, local links, A4 SVG semantics, searchable one-page PDFs, exact integer set/branch results and SHA-256 file hashes. python3 print/generate_print.py --write regenerates the aids and alternatives. Inspect rendered PDF pages visually too; text extraction cannot detect every alignment error. Teachers should pilot pacing and wording with actual learners and recheck the live syllabus before future reuse.