Date: 29 September 2026. This is an author simulation and local file/browser inspection, not a classroom trial, independent mathematics review, assistive-technology study, real measurement or funder evaluation. No learner outcomes or live site deployment are claimed.
Teacher path
I opened Day 2, Card B, and the square-factor A4 mat. I could model 72=36×2, ask learners to produce 6sqrt(2), then check by squaring before giving an optional new context. The five time blocks add to 25 minutes and identify a next move for the common false sum rule. On Day 5, the new Check A values are separate from all card and swap values, and a 12-minute first-response window precedes the public key. In a real class I would adjust duration after seeing prior algebra knowledge.
Learner path
I solved Check A on paper before opening the key: sqrt(243)=9sqrt(3), sqrt(48)=4sqrt(3), so difference 5sqrt(3)≈8.7 cm. I tested the proposed sqrt(195) by squaring both positive expressions: 75 and 195 are unequal. I then used the labelled-point route on Check B: zeros 2 and 8, midpoint axis 5, vertex (5,9), y-intercept (0,-16), graph positive for 2<x<8; the independent ratio becomes 5sqrt(11)/11. This confirmed the key values, not learner usability.
Supporter/funder path
From README, a supporter can find ten clean cards, public feedback checks, separate key, optional swaps, complete print text, and a paper route for the offline aid. The source crosswalk exposes the exact v1.3 syllabus, page positions, sub-topic hours and unfinished quadratic work. A funder can inspect SHA-256 hashes and original asset rights. The pack does not claim a completed topic, actual workplace data, secure assessment, or measured learning gains.
Visual, interactive and arithmetic inspection
I rendered all five PDFs to images at 700-pixel height and inspected a contact sheet. Titles, exact/approx notation, worked examples, tactile lines and the five-point parabola stayed on-page with no observed clipping. The PDF text is selectable, every sheet is A4, and the graph's coordinates and axis are reproduced in full text. This is visual inspection, not user testing with low-vision or blind learners.
I opened the offline square-factor explorer in a headless browser with sample inputs 72, 18, 200, 1, 0 and 243; outputs matched expected exact forms (6sqrt(2), 3sqrt(2), 10sqrt(2), 1, validation message, 9sqrt(3)). I also inspected a full-page browser screenshot: controls, result, and paper route were visible at desktop size. The explorer uses no network request and makes no data claim beyond 1–5000 positive integers. The verifier checks lesson counts, links, source pin, known exact results, assets, interactive structure and file hashes.
Critique and next work
- Eight surd sessions give 3h20, under the syllabus' 4 notional hours; the teacher should revisit division, rationalisation, fluency and error diagnosis rather than treat this as certified coverage.
- Two quadratic sessions introduce features of vertex and factor forms. The 7-hour sub-topic still needs general form, equation methods, completing the square, quadratic formula, discriminant, technology and genuine modelling with data.
- The three routes demand identical exact notation and explanation but were simulated by an adult author. Teachers should adapt access and pacing after observing their own learners; route choice should not be assigned by a fixed learner label.
- Contexts are invented to keep the materials freely usable and avoid false claims about measured objects. An actual modelling task needs real data, assumptions and review of model limits.