Below is a printable table (suitable for copying into Excel) with one row per chapter-subtopic. Columns: Chapter, Subtopic, Best‑fit Year(s) (ACARA Years 7–10), ACARA Strand, ACARA‑style content wording, One‑line justification, ACARA match level, Selected Common Core Standard(s), Common Core match & one‑line justification.
| Chapter | Subtopic | Best‑fit Year(s) | ACARA Strand | ACARA‑style content wording | One‑line justification | ACARA match level | Selected Common Core Standard(s) | Common Core match & one‑line justification |
|---|---|---|---|---|---|---|---|---|
| 12 | Right Triangles and Quadrilaterals (overview) | Year 8 (primary), Year 7–9 (overview) | Measurement & Geometry; Working Mathematically | Investigate properties of right triangles and quadrilaterals and apply appropriate measurement and reasoning strategies to solve related problems. | Chapter ties core geometry of right triangles and quadrilaterals to measurement and problem solving. | Direct match | 6.G.1; Grade 7 geometry cluster; 8.G.5–8.G.7 | 6.G.1 and 8.G.5–8.G.7: Partial–Direct (overview connects to these standards; detailed theorems map best to Year 8 CC geometry standards). |
| 12 | The Pythagorean Theorem | Year 8 | Measurement & Geometry | Apply Pythagoras' theorem to determine unknown side lengths in right‑angled triangles and solve related measurement problems. | Direct teaching and application of the Pythagorean theorem to compute side lengths. | Direct match | 8.G.6; 8.G.7; (6.G.1 partial) | 8.G.6: Direct — uses/teaches Pythagorean theorem; 8.G.7: Partial — applies to coordinate contexts if included; 6.G.1: Partial (area/triangle decomposition linkage). |
| 12 | Pythagorean triples | Year 9 (extension) / Year 8 (investigation) | Number & Algebra; Measurement & Geometry | Investigate integer solutions to a^2 + b^2 = c^2 (Pythagorean triples), generate examples and explore properties. | Develops number‑theoretic exploration built on the Pythagorean theorem; goes beyond routine application. | Extension / exceeds year expectations | 8.G.6 (conceptual link); Grade 7 geometry cluster (investigation) | 8.G.6: Partial — logical extension of Pythagorean ideas; High‑school number/algebra standards: Extension — more number theory than typical MS geometry standards. |
| 12 | 30°‑60°‑90° and 45°‑45°‑90° triangles | Year 9 (partial) / Year 8 (introduction) | Measurement & Geometry; Number & Algebra | Use special right triangle ratios (1:√3:2 and 1:1:√2) to find side lengths and solve geometric problems efficiently. | Introduces specific ratio patterns and exact values for standard right triangles useful for problem solving. | Partial match | Grade 7 geometry cluster; 8.G.5–8.G.7 (similarity & triangle properties) | 7th/8th cluster: Partial — connects to similarity and proportional reasoning; often exceeds routine middle school expectations by emphasizing exact radicals and ratio patterns. |
| 12 | Types of quadrilaterals | Year 7 | Measurement & Geometry | Classify and describe properties of quadrilaterals (parallelogram, rectangle, rhombus, square, trapezium) and relate side/angle properties. | Directly addresses classification and properties of quadrilaterals typical of Year 7 geometry. | Direct match | Grade 7 geometry cluster; 6.G.1 (contextual) | Grade 7 cluster: Direct — classification and properties align well; 6.G.1: Partial (area/shape decomposition links). |
| 12 | Quadrilateral area | Year 7–8 | Measurement & Geometry | Calculate area of quadrilaterals by decomposition into triangles/rectangles and apply formulas in problem contexts. | Uses decomposition and standard formulas to find areas — matches ACARA focus on measurement and problem solving. | Direct match | 6.G.1; Grade 7 geometry cluster | 6.G.1: Direct — composition/decomposition of shapes to find triangular/quadrilateral area; Grade 7: Partial — supports reasoning and application. |
| 15 | Find a pattern | Years 7–10 (Working Mathematically across years) | Working Mathematically; Number & Algebra | Identify and generalise numerical or geometric patterns to make conjectures and solve problems. | Pattern finding is a core mathematical strategy emphasised in the Working Mathematically strand across Years 7–10. | Direct match | A‑SSE.1 (structure); A‑CED.1 (modeling), S‑ID.1–S‑ID.3 (where patterns in data apply) | A‑SSE.1 / A‑CED.1: Partial‑Direct — pattern recognition supports creating/structuring expressions and models; S‑ID: Partial when patterns arise in data contexts. |
| 15 | Make a list | Years 7–10 (Working Mathematically) | Working Mathematically; Number & Algebra | Systematically list possibilities or cases to ensure completeness when solving combinatorial or enumeration problems. | Cataloguing cases is an explicit problem‑solving strategy in ACARA's Working Mathematically across middle secondary years. | Direct match | S‑ID.1–S‑ID.3 (data organization); A‑CED.1 (constructing models) | S‑ID / A‑CED: Partial — listing supports data/tabulation and equation building but is a general strategy rather than a content standard itself. |
| 15 | Draw a picture | Years 7–10 (Working Mathematically) | Working Mathematically; Measurement & Geometry | Use diagrams and scaled sketches to represent problems, clarify relationships and support solution strategies. | Drawing is a central heuristic in ACARA problem solving and geometry work at these levels. | Direct match | 8.G.5–8.G.7; A‑CED.1; S‑ID.1 | 8.G.5–8.G.7: Partial — diagrams support similarity/triangle reasoning; A‑CED.1 / S‑ID.1: Partial — diagrams assist in modeling and data representation. |
| 15 | Work backwards | Years 7–10 (Working Mathematically) | Working Mathematically; Number & Algebra | Solve problems by starting from the desired result and reversing operations or steps to find the unknown starting conditions. | Backwards reasoning is a standard problem‑solving strategy explicitly encouraged in ACARA problem solving strands. | Direct match | A‑CED.1; N‑Q.3; S‑ID.1–S‑ID.3 | A‑CED.1: Direct — useful for creating equations and solving for unknowns; N‑Q.3: Partial — choosing accuracy relates to solution interpretation; S‑ID: Partial for reverse‑engineering data models. |
Notes for use and printing:
- Copy the HTML table into a simple HTML file and open in a browser, then use Print > Save as PDF or Print to your printer; or paste the table into Excel by selecting the table and pasting into a spreadsheet.
- Each row is one chapter subtopic; the Best‑fit Year(s) column indicates where the content naturally sits in the ACARA Year 7–10 progression.
- ACARA wording is written in an ACARA‑style (descriptive) form rather than quoting official ACARA codes; for formal curriculum mapping you may wish to match the descriptors to exact ACARA content codes in your jurisdiction.
- Common Core references are to the selected standards you requested (6.G.1; Grade 7 geometry cluster; 8.G.5–8.G.7; and selected HS standards N‑Q.3, A‑SSE.1, A‑CED.1, S‑ID.1–S‑ID.3). Match levels indicate whether the chapter content is a direct match, partial connection, or an extension beyond those standards.
If you would like a downloadable .xlsx file prepared with these rows (one worksheet per chapter, formatted for printing), say the word and I will generate it.