Checked 29 September 2026 on the official QCAA Essential Mathematics page and Essential Mathematics 2025 v1.3 Applied (Essential) senior syllabus, published January 2026. The page says this syllabus applies to students completing the course in 2026 or later. This pathway is distinct from General Mathematics and is not taken by every Year 11 student. It is a QCAA senior syllabus, not an ACARA P–10 code list. EM-U1-T1-R is local SubjectNest shorthand, not an official QCAA code. source-snapshot.json records source identity and pages.
QCAA places Unit 1: Number, data and money at PDF p. 16 / printed p. 14. At PDF p. 17 / printed p. 15 it says the Fundamental topic Calculations is integrated through Unit 1, and Topic 1 Number starts with Ratios (7 hours). These ten planned sessions are 250 minutes = 4 hours 10 minutes, below the 7-hour notional ratio subtopic even before considering whether students learned it. Rates, Percentages and Units of energy are later Topic 1 subtopics. Topic 2 Representing data, Topic 3 Managing money, the rest of Unit 1 and Units 2–4 are outside this starter. A unit has 55 notional hours including assessment. The syllabus encourages contexts meaningful to the student cohort; our cases span paper design, theatre, library, workshop and sketching without requiring personal financial data.
Printed page 15 ratio subject-matter map
Bullet numbers below follow the official Ratios subtopic's order. We paraphrase its wording and point teachers to the official PDF; a teaching prompt is opportunity, not proof of mastery. QCAA marks bullets 5 and 6 [complex], so this pack introduces them but does not claim full complex-problem proficiency.
| QCAA printed p. 15 row | Source focus, paraphrased | Observable opportunity in this starter | Boundary |
|---|---|---|---|
| Ratios bullet 1 | Ideas and notation of ratio. | Days 1–2 order labelled parts; Check A writes both orders. | Short invented symbol sets do not cover every context. |
| Ratios bullet 2 | Relationship of fractions to ratios. | Day 3 part-to-part versus part-to-all; Day 9 claim audit; Check A. | Learners must name the whole; a correct numeral alone does not show interpretation. |
| Ratios bullet 3 | Simplest whole-number ratio. | Day 4 common factor and reverse; Days 6, 9; Check A. | Requires evidence across other values and representations. |
| Ratios bullet 4 | Simplest ratio of two quantities. | Day 6 converts 1 m to 100 cm before comparing with 150 cm. | A single length example does not cover varied units and quantities. |
| Ratios bullet 5 [complex] | Divide a total in a given ratio. | Day 7 five equal parts; Day 9 rescale; Check B new total/ratio. | These are scaffolded, fully specified cases. They do not establish complex unfamiliar problem solving. |
| Ratios bullet 6 [complex] | Describe simple scales with ratio. | Day 8 1 cm:200 cm invented sketch and reverse check; Check B new scale. |
A paper plan is not an actual measurement, and two simple examples do not establish complex scale modelling. |
At printed p. 15 the Fundamental topic Calculations lists ten bullet groups: basic number operations; order of operations; reasonableness; leading-digit estimates; calculator use for multi-step work; accuracy checks; decimal place value; evaluation to required decimal places; rounding; and approximation. This pack integrates the basic operations, order, reasonableness, calculator option and reverse checks in Days 3–10. It does not explicitly assess leading-digit estimation, decimal-place interpretation or rounding. They require further instruction. No claim is made that this fortnight covers the entire Fundamental topic.
The syllabus's printed p. 5 gives school requirements for Unit 1–2 assessment; its formal decisions are made by the school within those requirements. Our public Day 5/10 checks are two short formative teaching observations, not school-designed formal instruments, QCAA common assessment, secure exams or grades. Their public key means a teacher should keep first responses and use unseen local variants when needed. No external classroom validation, assessment moderation or QCAA endorsement is claimed.
Source and fact ledger
| Claim or material | Provenance and limit |
|---|---|
| Current version, Applied (Essential) pathway, Unit 1/Topic 1/Ratios sequence, 7-hour notional time, [complex] markers and Fundamental Calculations | Official QCAA syllabus, PDF pp. 6–7, 16–17 / printed pp. 4–5, 14–15, and subject page. All mappings here are our own paraphrases and limited alignment judgments. |
| Tokens, tags, labels, quantities, scales, drawings, examples and check values | Original fictional teaching inputs in this pack. The sketch is not a measured or approved plan. Results are recomputed by the local verifier. |
| External text/artwork | No QCAA logo, third-party image, prior assessment question, student work, translation or First Nations cultural material is included. Rights ledger separates sources and original assets. |
The official PDF was read through QCAA's rendered web result. Direct command-line download returned HTTP 403, so no byte hash of the QCAA PDF is claimed. The verifier pins the dated source facts and hashes our authored files; it cannot verify future live-page changes. Recheck the official page before later reuse. QCAA source attribution: © State of Queensland (QCAA) 2026, subject to its copyright conditions. QCAA has not reviewed or endorsed this pack.