Below is a chapter-by-chapter mapping (Chapters 9–12) of the Prealgebra text (ISBN 978-1-934124-21-5) to ACARA-style content descriptions for Years 7–10. Each row corresponds to one chapter subtopic and includes: Year, Strand, ACARA-style content wording, a one-line justification for the mapping, and a match level: “Direct match”, “Partial match”, or “Extension / exceeds year expectations.”
How to use
- To print or open in Excel: copy the CSV block below into a text file and save as file.csv (or import into Excel directly).
- Alternatively, copy the HTML table below and paste into a browser or into a document for printing.
CSV (copy everything between the --- lines and save as .csv)
--- "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 and represent square numbers and their square roots; use index notation for squares and square roots.","Introduces the concept and notation of square roots and squares as taught when students learn indices/square numbers.","Direct match" "9 - Square Roots","Equations with square roots","Year 9","Number and Algebra","Solve simple equations by extracting square roots (e.g. x^2 = a) and interpret principal square root.","Solving equations by root extraction aligns with Year 9 work on solving simple equations including those involving powers.","Direct match" "9 - Square Roots","Non-integer square roots","Year 9","Number and Algebra","Approximate non-integer square roots (using calculators or numerical methods) and relate to real numbers and decimal representations.","Text treats approximate roots and numeric methods which matches Year 9 expectations for approximating irrational results; exact surd work may extend further.","Partial match" "9 - Square Roots","Simplification of square roots","Year 9","Number and Algebra","Simplify numerical expressions involving square roots (express roots of perfect squares and simplify simple radical expressions).","Simplifying radicals of integers aligns well with Year 9 content on indices and exact forms.","Direct match" "9 - Square Roots","Arithmetic with square roots","Year 10","Number and Algebra","Perform arithmetic with surds (add, subtract, multiply), simplify products and quotients of square roots, recognize exact and approximate forms.","Operations with surds and manipulation to exact form goes beyond basic Year 9 simplification and is typically treated more fully at Year 10 or in extension work.","Extension / exceeds year expectations" "10 - Angles","Angle measurement","Year 7","Measurement and Geometry","Measure and construct angles, compare and classify angles using degrees; use protractors to estimate and measure.","Fundamental angle measurement and use of protractors is a core Year 7 measurement topic.","Direct match" "10 - Angles","Parallel lines","Year 8","Measurement and Geometry","Use properties of parallel lines and transversals to identify corresponding, alternate and co-interior angles and solve angle problems.","Identifying angle relationships created by parallel lines is standard Year 8 geometry content.","Direct match" "10 - Angles","Angles in a triangle","Year 7","Measurement and Geometry","Use properties of triangles, including the sum of interior angles equals 180°, to find missing angles and reason about triangle geometry.","Sum of interior angles and basic triangle angle reasoning is typically introduced in Year 7/8; mapped to Year 7 here as core.","Direct match" "10 - Angles","Angles in other polygons","Year 8","Measurement and Geometry","Investigate and use formulas for the sum of interior angles of polygons and calculate interior/exterior angles of regular polygons.","Working with interior angle sums and regular polygon angle measures aligns with Year 8 geometry outcomes.","Direct match" "11 - Perimeter and Area","Segments and perimeter","Year 7","Measurement and Geometry","Explore and calculate perimeters of plane figures, including composite shapes; use units and add segment lengths.","Perimeter of polygons and composite shapes is expected in Year 7 measurement content.","Direct match" "11 - Perimeter and Area","Triangle inequality","Year 9","Number and Algebra / Measurement and Geometry","Investigate and apply the triangle inequality theorem to determine possible side lengths; reason about existence of triangles.","Triangle inequality reasoning appears as a more formal geometric/number property suited to Year 9 level reasoning; textbooks treat it as an extension of basic triangle properties.","Partial match" "11 - Perimeter and Area","Triangle area","Year 7","Measurement and Geometry","Apply formula for area of a triangle (1/2 * base * height) and use it to solve problems involving triangles and composite figures.","Computing triangle area using base and height is covered in Year 7–8 measurement topics; direct alignment with Year 7 introductory area work.","Direct match" "11 - Perimeter and Area","Circumference of a circle","Year 8","Measurement and Geometry","Use π to calculate circumference of circles and relate diameter and radius to circumference measurements.","Computing circumference and relating radius/diameter to circumference is a Year 8 measurement expectation.","Direct match" "11 - Perimeter and Area","Area of a circle","Year 8","Measurement and Geometry","Use π to calculate the area of a circle and solve problems involving circle area in context.","Area of a circle is standard Year 8 content alongside circumference.","Direct match" "11 - Perimeter and Area","Unusual areas (composite, sectors, segments)","Year 10","Measurement and Geometry","Calculate areas of composite shapes, circle sectors and segments, and use decomposition/recombination to solve non-standard area problems.","Working with sectors, circular segments, and complex composite areas typically extends beyond Year 8 basics and aligns with Year 10 problem-solving requirements.","Partial match" "12 - Right Triangles and Quadrilaterals","The Pythagorean Theorem","Year 8","Measurement and Geometry","Use the Pythagorean theorem to determine lengths in right-angled triangles and solve related problems in two dimensions.","Pythagoras for numerical length problems is a common Year 8–9 curriculum topic; direct alignment with Year 8 introduction and Year 9 applications.","Direct match" "12 - Right Triangles and Quadrilaterals","Pythagorean triples","Year 9","Number and Algebra","Investigate integer solutions (Pythagorean triples) and use them to generate examples of right triangles with integer side lengths.","Exploring integer triples and their generation is an enrichment/extension of the Pythagorean theorem but is covered at middle secondary levels.","Partial match" "12 - Right Triangles and Quadrilaterals","30-60-90 and 45-45-90 triangles","Year 10","Measurement and Geometry / Number and Algebra","Use properties of special right triangles to determine exact side ratios and solve problems without a calculator, linking to trigonometric reasoning.","Special right-triangle ratios move toward Year 10 trigonometric and ratio expectations and often exceed earlier year expectations for exact-value reasoning.","Extension / exceeds year expectations" "12 - Right Triangles and Quadrilaterals","Types of quadrilaterals","Year 7","Measurement and Geometry","Classify and describe quadrilaterals (parallelograms, rectangles, rhombuses, trapezia) using their properties (parallel sides, equal angles, symmetry).","Classification by properties is core Year 7–8 geometry material; direct match with introductory quadrilateral work.","Direct match" "12 - Right Triangles and Quadrilaterals","Quadrilateral area","Year 8","Measurement and Geometry","Calculate areas of common quadrilaterals (parallelogram, trapezium, kite) and use decomposition for irregular shapes.","Area formulas for quadrilaterals and decomposition strategies align with Year 8 measurement expectations.","Direct match" ---
HTML preview table (for printing or copying into a document)
| 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 and represent square numbers and their square roots; use index notation for squares and square roots. | Introduces the concept and notation of square roots and squares as taught when students learn indices/square numbers. | Direct match |
| 9 - Square Roots | Equations with square roots | Year 9 | Number and Algebra | Solve simple equations by extracting square roots (e.g. x^2 = a) and interpret principal square root. | Solving equations by root extraction aligns with Year 9 work on solving simple equations including those involving powers. | Direct match |
| 9 - Square Roots | Non-integer square roots | Year 9 | Number and Algebra | Approximate non-integer square roots (using calculators or numerical methods) and relate to real numbers and decimal representations. | Text treats approximate roots and numeric methods which matches Year 9 expectations for approximating irrational results; exact surd work may extend further. | Partial match |
| 9 - Square Roots | Simplification of square roots | Year 9 | Number and Algebra | Simplify numerical expressions involving square roots (express roots of perfect squares and simplify simple radical expressions). | Simplifying radicals of integers aligns well with Year 9 content on indices and exact forms. | Direct match |
| 9 - Square Roots | Arithmetic with square roots | Year 10 | Number and Algebra | Perform arithmetic with surds (add, subtract, multiply), simplify products and quotients of square roots, recognize exact and approximate forms. | Operations with surds and manipulation to exact form goes beyond basic Year 9 simplification and is typically treated more fully at Year 10 or in extension work. | Extension / exceeds year expectations |
| 10 - Angles | Angle measurement | Year 7 | Measurement and Geometry | Measure and construct angles, compare and classify angles using degrees; use protractors to estimate and measure. | Fundamental angle measurement and use of protractors is a core Year 7 measurement topic. | Direct match |
| 10 - Angles | Parallel lines | Year 8 | Measurement and Geometry | Use properties of parallel lines and transversals to identify corresponding, alternate and co-interior angles and solve angle problems. | Identifying angle relationships created by parallel lines is standard Year 8 geometry content. | Direct match |
| 10 - Angles | Angles in a triangle | Year 7 | Measurement and Geometry | Use properties of triangles, including the sum of interior angles equals 180°, to find missing angles and reason about triangle geometry. | Sum of interior angles and basic triangle angle reasoning is typically introduced in Year 7/8; mapped to Year 7 here as core. | Direct match |
| 10 - Angles | Angles in other polygons | Year 8 | Measurement and Geometry | Investigate and use formulas for the sum of interior angles of polygons and calculate interior/exterior angles of regular polygons. | Working with interior angle sums and regular polygon angle measures aligns with Year 8 geometry outcomes. | Direct match |
| 11 - Perimeter and Area | Segments and perimeter | Year 7 | Measurement and Geometry | Explore and calculate perimeters of plane figures, including composite shapes; use units and add segment lengths. | Perimeter of polygons and composite shapes is expected in Year 7 measurement content. | Direct match |
| 11 - Perimeter and Area | Triangle inequality | Year 9 | Number and Algebra / Measurement and Geometry | Investigate and apply the triangle inequality theorem to determine possible side lengths; reason about existence of triangles. | Triangle inequality reasoning appears as a more formal geometric/number property suited to Year 9 level reasoning; textbooks treat it as an extension of basic triangle properties. | Partial match |
| 11 - Perimeter and Area | Triangle area | Year 7 | Measurement and Geometry | Apply formula for area of a triangle (1/2 * base * height) and use it to solve problems involving triangles and composite figures. | Computing triangle area using base and height is covered in Year 7–8 measurement topics; direct alignment with Year 7 introductory area work. | Direct match |
| 11 - Perimeter and Area | Circumference of a circle | Year 8 | Measurement and Geometry | Use π to calculate circumference of circles and relate diameter and radius to circumference measurements. | Computing circumference and relating radius/diameter to circumference is a Year 8 measurement expectation. | Direct match |
| 11 - Perimeter and Area | Area of a circle | Year 8 | Measurement and Geometry | Use π to calculate the area of a circle and solve problems involving circle area in context. | Area of a circle is standard Year 8 content alongside circumference. | Direct match |
| 11 - Perimeter and Area | Unusual areas (composite, sectors, segments) | Year 10 | Measurement and Geometry | Calculate areas of composite shapes, circle sectors and segments, and use decomposition/recombination to solve non-standard area problems. | Working with sectors, circular segments, and complex composite areas typically extends beyond Year 8 basics and aligns with Year 10 problem-solving requirements. | Partial match |
| 12 - Right Triangles and Quadrilaterals | The Pythagorean Theorem | Year 8 | Measurement and Geometry | Use the Pythagorean theorem to determine lengths in right-angled triangles and solve related problems in two dimensions. | Pythagoras for numerical length problems is a common Year 8–9 curriculum topic; direct alignment with Year 8 introduction and Year 9 applications. | Direct match |
| 12 - Right Triangles and Quadrilaterals | Pythagorean triples | Year 9 | Number and Algebra | Investigate integer solutions (Pythagorean triples) and use them to generate examples of right triangles with integer side lengths. | Exploring integer triples and their generation is an enrichment/extension of the Pythagorean theorem but is covered at middle secondary levels. | Partial match |
| 12 - Right Triangles and Quadrilaterals | 30-60-90 and 45-45-90 triangles | Year 10 | Measurement and Geometry / Number and Algebra | Use properties of special right triangles to determine exact side ratios and solve problems without a calculator, linking to trigonometric reasoning. | Special right-triangle ratios move toward Year 10 trigonometric and ratio expectations and often exceed earlier year expectations for exact-value reasoning. | Extension / exceeds year expectations |
| 12 - Right Triangles and Quadrilaterals | Types of quadrilaterals | Year 7 | Measurement and Geometry | Classify and describe quadrilaterals (parallelograms, rectangles, rhombuses, trapezia) using their properties (parallel sides, equal angles, symmetry). | Classification by properties is core Year 7–8 geometry material; direct match with introductory quadrilateral work. | Direct match |
| 12 - Right Triangles and Quadrilaterals | Quadrilateral area | Year 8 | Measurement and Geometry | Calculate areas of common quadrilaterals (parallelogram, trapezium, kite) and use decomposition for irregular shapes. | Area formulas for quadrilaterals and decomposition strategies align with Year 8 measurement expectations. | Direct match |
Notes on mapping decisions (brief):
- ACARA has a clear progression from Year 7 introduction to indices, angle measurement, and basic area/perimeter up to Year 10 problem-solving with more abstract exact forms and trigonometric links. I mapped core definitions and basic procedures to Years 7–9 where appropriate and placed more advanced exact/surd/trigonometric material at Year 10 as Extension.
- Where the textbook treats advanced manipulations (surds arithmetic, exact side ratios from special triangles, sector/segment area techniques) I marked these as Partial or Extension because they exceed the most basic Year 7–8 outcomes and more closely align with Year 10 or enrichment material.
- If you want the mapping with official ACARA content descriptor codes (e.g., MA7/MA8 codes) I can add likely code matches — but I have provided ACARA-style wording rather than official code references to avoid inaccuracies in exact code assignment.
If you would like, I can:
- Produce the same table with official ACARA content descriptor codes appended (I will identify likely matching codes for each item), or
- Provide a downloadable Excel (.xlsx) file (I can produce the file content and instructions so you can download it), or
- Map additional chapters (1–8, 13–15) in the same format.
Which of these would you like next?