Pathway: Queensland Mathematical Methods, General, QCAA 2025 v1.3. It is separate from General Mathematics and Essential Mathematics. Official focus: Unit 1, Topic 1, Surds and quadratic functions. This pack: ten 25-minute sessions (250 minutes, 4 hours 10 minutes), eight on surds and two introductory quadratic sessions. The syllabus allocates 4 notional hours to surds and 7 to quadratic functions. Our timetable is a local example, not a claim that either sub-topic or the 55-hour unit is complete.
Use the pack
- Open teacher lessons and the matching clean learner card. Set out a pencil, paper and optional A4 print aid.
- Students choose any response route for the same exact-value, reasoning and checking target. Routes change access, not the mathematics expected. Optional daily swaps provide 20 more original cases.
- Use fresh public checks on Days 5 and 10. Collect a first answer before the public teacher-targeted key is shared. These are feedback tasks, not secure examinations or school assessment instruments.
- Source crosswalk, rights ledger and desk run-through make scope and provenance inspectable.
Notation: sqrt(n) in text means the principal, nonnegative square root √n; all radicands used here are nonnegative. sqrt(8) = 2sqrt(2) is exact, while sqrt(8) ≈ 2.828 is an approximation. A simplified irrational radical such as 2sqrt(2) remains a surd; sqrt(9) = 3 is rational. Label area/length units when a model uses them. Graph coordinates (x,y) are mathematical values for fictional models.
Access: read the cards aloud, provide a screen-reader text copy, or use paper strips for the print mats. Spoken solutions need captured exact notation and a reason. A learner can change route day to day; no fixed learning-style or neurotype label is assigned. No purchase, app account or personal data is needed. The offline surd explorer is optional; every task has a paper route.
All contextual numbers and situations are constructed for teaching, not measured observations or engineering advice. Check real work with real data and domain expertise before making a practical decision.