Thanks — I can produce a full alignment of Art of Problem Solving (AoPS) Prealgebra 1 & 2 chapter topics to ACARA content descriptions and provide the precise ACARA codes. Before I produce the complete table with codes, please confirm which ACARA release you want me to use:
- AC v8.x (common references use codes beginning with ACMNA, ACMMG, ACMSP, etc.) — this is the widely used version in many schools and published resources.
- AC v9 (newer release that uses a revised code system) — I can map to the v9 codes if that is what you need.
If you aren’t sure, tell me the state (e.g. NSW, VIC) or the syllabus version you use and I’ll pick the most common mapping. Once you confirm, I will return a complete Year 7–10 mapping that lists, for each AoPS chapter:
- The matching ACARA content descriptions (full text)
- The exact ACARA code(s) for your requested AC version
- The suggested Year level(s) (7, 8, 9, 10) where that AoPS topic best fits
- Notes on teaching emphasis and any gaps or extensions
Below is a concise sample mapping (no codes yet) to show the format and the likely Year-level placements for each AoPS chapter topic. This sample helps you confirm that the approach and grouping meet your needs.
Sample mapping: AoPS Prealgebra 1 (Chapters 1–7)
- 1 — Properties of Arithmetic (rigorous arithmetic basics; arithmetic rules)
- Suggested Years: 7–8
- ACARA strand alignment: Number and Algebra – Number & Algebraic thinking
- Typical ACARA content descriptions (by topic): place value and properties of operations, order of operations, associative/commutative/distributive reasoning, rewriting and simplifying arithmetic expressions.
- Teaching notes: emphasize structure that supports algebraic generalisation used later in equations and algebra.
- 2 — Exponents (laws, zero, negative exponents)
- Suggested Years: 8–9
- ACARA strand alignment: Number and Algebra – Number
- Typical ACARA content descriptions: integer powers and index notation, laws of exponents, positive/zero/negative integer powers, simplifying expressions involving powers.
- Teaching notes: connects strongly with scientific notation and algebraic manipulation in Year 9–10.
- 3 — Number Theory (multiples, divisibility, primes, factorisation, LCM, GCD)
- Suggested Years: 7–9
- ACARA strand alignment: Number and Algebra – Number
- Typical ACARA content descriptions: divisibility tests, prime and composite numbers, prime factorisation, use of factors for LCM/GCF problems.
- Teaching notes: strong fit for problem solving and for later algebraic factorisation ideas.
- 4 — Fractions (definition, arithmetic, comparison, mixed numbers)
- Suggested Years: 7–8
- ACARA strand alignment: Number and Algebra – Number
- Typical ACARA content descriptions: operations with fractions, simplifying, converting between improper/mixed, problem solving with fractions.
- 5 — Equations and Inequalities (expressions, linear equations, word problems, linear inequalities)
- Suggested Years: 8–9
- ACARA strand alignment: Number and Algebra – Algebra
- Typical ACARA content descriptions: forming and solving linear equations, using algebraic notation, solving linear inequalities and interpreting solutions in context.
- 6 — Decimals (notation, arithmetic, conversion, rational/decimal forms)
- Suggested Years: 7–8
- ACARA strand alignment: Number and Algebra – Number
- Typical ACARA content descriptions: decimal place value, addition/subtraction/multiplication/division of decimals, converting between fractions and decimals, terminating vs repeating decimals.
- 7 — Ratios, Conversions, and Rates (ratio & proportion, unit conversion, speed/distance/time)
- Suggested Years: 7–9
- ACARA strand alignment: Number and Algebra – Measurement & Geometry overlap for rate contexts
- Typical ACARA content descriptions: ratio notation and reasoning, solving proportion problems, using unit conversion factors, simple rate problems including average speed and work.
Sample mapping: AoPS Prealgebra 2 (Chapters 8–15)
- 8 — Percents (percent–fraction–decimal relationships, percent change)
- Suggested Years: 7–8
- ACARA strand alignment: Number and Algebra
- Typical ACARA content descriptions: converting between percentages, fractions and decimals, percentage problems, percent increase/decrease and simple compound examples.
- 9 — Square Roots (definition, simplification, arithmetic)
- Suggested Years: 8–9
- ACARA strand alignment: Number and Algebra — Number
- Typical ACARA content descriptions: square roots and squares, simplifying square root expressions, solving simple equations involving square roots (leading to Pythagoras later).
- 10 — Angles (measurement, parallel lines, triangle angles, polygons)
- Suggested Years: 7–8
- ACARA strand alignment: Measurement & Geometry
- Typical ACARA content descriptions: angle measurement, relationships of angles formed by parallel lines and transversals, interior/exterior angles of polygons, angle sum in triangles.
- 11 — Perimeter and Area (segments, triangle inequality, triangle area, circle area)
- Suggested Years: 7–9
- ACARA strand alignment: Measurement & Geometry
- Typical ACARA content descriptions: perimeter and area formulae for polygons and circles, triangle inequality, deriving area of triangles/circles, compound areas and unusual shapes.
- 12 — Right Triangles and Quadrilaterals (Pythagoras, special right triangles, quadrilateral types, area)
- Suggested Years: 8–9 (Pythagoras often Year 8); extension into Year 10 for proofs/coordinate forms)
- ACARA strand alignment: Measurement & Geometry
- Typical ACARA content descriptions: Pythagorean theorem and applications, identifying right-triangle side relationships, properties and area formulae for quadrilaterals.
- 13 — Data and Statistics (mean, median, mode, range, graphs)
- Suggested Years: 7–9
- ACARA strand alignment: Statistics & Probability
- Typical ACARA content descriptions: centre and spread measures, interpreting data displays, limitations of simple statistics and choice of summary measure.
- 14 — Counting (lists, Venn diagrams, multiplication principle, casework, intro to probability)
- Suggested Years: 8–10
- ACARA strand alignment: Statistics & Probability and Number & Algebra (combinatorics/intro probability)
- Typical ACARA content descriptions: systematic counting strategies, basic probability with sample spaces, Venn diagram use for sets and counting overlaps.
- 15 — Problem-Solving Strategies (pattern, lists, drawings, work backwards)
- Suggested Years: 7–10 (cross-year thinking skill)
- ACARA strand alignment: General proficiencies — problem solving and reasoning apply across the curriculum
- Typical ACARA content descriptions: problem-solving strategies and working mathematically expectations; reasoning and communicating mathematical ideas.
Next steps I can do for you:
- Map every AoPS chapter topic to the exact ACARA content descriptions and return the precise ACARA codes for either AC v8.x or AC v9 — choose which version.
- Produce the alignment as a CSV or spreadsheet (columns: AoPS chapter, AoPS subtopics, ACARA code, ACARA description text, suggested Year level, teaching notes, assessment ideas).
- Highlight any AoPS topics that are above Year 10 level or that could be split across multiple Year levels, and suggest sequencing across Years 7–10.
Please tell me which ACARA version you want (v8.x or v9) and whether you want the result as a spreadsheet or a plain table here. Once you confirm, I will deliver the complete mapping with exact ACARA codes and brief notes for each match.
If helpful, here is the official ACARA curriculum link (to search content descriptions): https://www.australiancurriculum.edu.au/