# Essential Mathematics QCAA source and honest partial crosswalk

Checked **29 September 2026** on the official [QCAA Essential Mathematics page](https://www.qcaa.qld.edu.au/senior/senior-subjects/syllabuses/mathematics/essential-mathematics) and [Essential Mathematics 2025 v1.3 Applied (Essential) senior syllabus](https://www.qcaa.qld.edu.au/downloads/senior-qce/syllabuses/snr_ess_maths_25_app_syll.pdf), 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](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](STUDENT-CHECKS.md) are two short **formative teaching observations**, not school-designed formal instruments, QCAA common assessment, secure exams or grades. Their [public key](teacher/KEY-AND-NEXT.md) 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](https://www.qcaa.qld.edu.au/downloads/senior-qce/syllabuses/snr_ess_maths_25_app_syll.pdf), PDF pp. 6–7, 16–17 / printed pp. 4–5, 14–15, and [subject page](https://www.qcaa.qld.edu.au/senior/senior-subjects/syllabuses/mathematics/essential-mathematics). 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](SOURCE-AND-RIGHTS.md) 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](verify_pack.py) 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](https://www.qcaa.qld.edu.au/copyright). QCAA has not reviewed or endorsed this pack.