Source: Prealgebra (Richard Rusczyk, David Patrick, Ravi Boppana), ISBN: 978-1-934124-21-5 — Chapters 1–15 (mapping provided here for Chapters 9–12).
| Chapter | Subtopic | Year | Strand | ACARA-style content wording | One-line justification | Match level |
|---|---|---|---|---|---|---|
| 9 — Square Roots | Definition of square root | Year 8 | Number and Algebra | Recognise square numbers and evaluate square roots of perfect squares; use and interpret √ notation. | Text introduces √ notation and perfect-square evaluation consistent with Year 8 objectives on squares and roots. | Direct match |
| 9 — Square Roots | Equations with square roots | Year 9 | Number and Algebra | Solve simple equations that include square roots (e.g. x^2 = k) and interpret positive/negative roots where appropriate. | Solving basic root equations aligns with Year 9 algebraic solution work though the book may go deeper in technique. | Partial match |
| 9 — Square Roots | Non-integer square roots | Year 9 | Number and Algebra / Real numbers | Approximate and represent non-integer square roots (recognise irrational square roots and use calculators or estimation). | Text treats approximate/irrational roots; ACARA introduces real-number concepts—alignment is partial because detail level may differ. | Partial match |
| 9 — Square Roots | Simplification of square roots | Year 9–10 | Number and Algebra | Simplify square roots by factoring (express √(a*b) as √a·√b where appropriate) and simplify surd expressions. | Book shows algebraic simplification of radicals; ACARA touches on manipulation of numerical and algebraic expressions—some content is more advanced. | Partial match |
| 9 — Square Roots | Arithmetic with square roots | Year 10 | Number and Algebra | Perform arithmetic operations with surds (add, subtract, multiply, rationalise simple denominators) and use laws of indices where relevant. | Operations on surds are more advanced than core lower-secondary content; the text covers methods beyond typical Years 7–9 expectations. | Extension / exceeds year expectations |
| 10 — Angles | Angle measurement | Year 7 | Measurement and Geometry | Estimate, measure and compare angles using degrees; use protractors and measure angles in geometric figures. | Direct coverage: the chapter’s angle measurement and practise with degrees aligns with Year 7 measurement outcomes. | Direct match |
| 10 — Angles | Parallel lines | Year 8 | Measurement and Geometry | Recognise and use angle relationships formed by parallel lines and a transversal (corresponding, alternate, interior angles). | Text develops transversal-angle relationships directly matching Year 8 expectations about parallel-line angle relationships. | Direct match |
| 10 — Angles | Angles in a triangle | Year 7–8 | Measurement and Geometry | Use the angle sum property of triangles (interior angles sum to 180°) to solve angle problems and find missing angles. | Triangle-angle-sum work is standard in Years 7–8 and the chapter’s examples map directly to that content. | Direct match |
| 10 — Angles | Angles in other polygons | Year 8–9 | Measurement and Geometry | Use interior-angle sum formula for polygons and apply to find individual or sum of angles in quadrilaterals and other polygons. | Chapter shows general polygon-angle reasoning and calculations; this aligns with Year 8–9 polygon angle content. | Direct match |
| 11 — Perimeter and Area | Segments and perimeter | Year 7 | Measurement and Geometry | Calculate perimeters of simple polygons by summing side lengths; understand segment notation and length measures. | Basic perimeter and segment measurement is core Year 7 content and the chapter covers these skills directly. | Direct match |
| 11 — Perimeter and Area | Triangle inequality | Year 9 | Number and Algebra / Measurement and Geometry | Investigate and apply the triangle inequality (sum of lengths of any two sides greater than the third) in geometric contexts. | Triangle inequality is more often treated as an extension/problem-solving topic; ACARA does not emphasize it at lower years—alignment is partial. | Partial match |
| 11 — Perimeter and Area | Triangle area | Year 8 | Measurement and Geometry | Use formula area = 1/2·base·height to calculate areas of triangles and solve related problems. | Direct correspondence: calculating triangle area using base and height is a Year 8 measurement outcome. | Direct match |
| 11 — Perimeter and Area | Circumference of a circle | Year 9 | Measurement and Geometry | Use circumference = 2πr (or πd) to calculate perimeter of circles and solve practical problems. | Chapter’s presentation of circle perimeter (circumference) aligns with Year 9 measurement of circular measures. | Direct match |
| 11 — Perimeter and Area | Area of a circle / Unusual areas | Year 9–10 | Measurement and Geometry | Use area = πr^2 for circles; determine areas of composite and non-standard shapes by decomposition or approximation. | Standard circle-area work maps to Year 9; composite/unusual areas extend problem-solving into Year 10-style challenges. | Direct match (circle area) / Partial to Extension (composite & unusual cases) |
| 12 — Right Triangles & Quadrilaterals | The Pythagorean Theorem | Year 8 | Measurement and Geometry | Apply Pythagoras' theorem to find side lengths in right-angled triangles and solve related measurement problems. | Direct alignment: Pythagoras is commonly taught at Year 8 and the chapter applies it in typical ways. | Direct match |
| 12 — Right Triangles & Quadrilaterals | Pythagorean triples | Year 9–10 | Number and Algebra / Measurement and Geometry | Investigate integer solutions to a^2 + b^2 = c^2 (Pythagorean triples) and use them in problem solving. | Exploration of integer triples is an enrichment/number-theory extension beyond core geometric uses of Pythagoras. | Extension / exceeds year expectations |
| 12 — Right Triangles & Quadrilaterals | 30-60-90 and 45-45-90 triangles | Year 10 | Measurement and Geometry / Number and Algebra | Recognise special right triangles and use their side ratios to solve geometric problems without trigonometry. | Special-triangle ratio results are typically beyond early secondary core but are useful in Year 10 problem solving—more advanced than basic geometry. | Extension / exceeds year expectations |
| 12 — Right Triangles & Quadrilaterals | Types of quadrilaterals | Year 7–8 | Measurement and Geometry | Classify quadrilaterals (parallelogram, rectangle, rhombus, square, trapezium) by sides, angles, and symmetry. | Describing and classifying quadrilaterals is a standard Year 7–8 geometry topic and the chapter follows this structure. | Direct match |
| 12 — Right Triangles & Quadrilaterals | Quadrilateral area | Year 8–9 | Measurement and Geometry | Calculate areas of parallelograms, trapezia and other quadrilaterals by decomposition or using base·height relationships. | Computing quadrilateral areas by decomposition and formulae aligns with Year 8–9 measurement expectations. | Direct match |
Notes on usage: Copy this HTML table into a spreadsheet (Excel, Google Sheets). Each table row is one chapter-subtopic mapped to Year, Strand, an ACARA-style content description, one-line justification, and a recommended match level. "Direct match" indicates close alignment with typical ACARA Year-level wording; "Partial match" indicates overlap but either different emphasis or depth; "Extension / exceeds year expectations" indicates material that generally goes beyond the listed Year-level expectations and could be used for enrichment.