| Chapter | Subtopic | Year | Strand | ACARA-style content wording | One-line justification | Match level |
|---|---|---|---|---|---|---|
| 1 | Rigorous definition of arithmetic basics | 7 | Number and Algebra | Describe and use the properties of the number system and operations (commutative, associative, distributive) and apply order of operations. | Core properties of operations and order of operations are Year 7 topics. | Direct match |
| 1 | Clever applications of arithmetic rules to make seemingly-complicated calculations simple | 8 | Number and Algebra | Apply arithmetic strategies and properties to simplify calculations and recognise patterns to solve non-routine problems. | Problem-solving with arithmetic strategies appears across Years 7–8; this emphasises efficient techniques beyond routine practice. | Partial match |
| 2 | Exponentiation and powers | 8 | Number and Algebra | Use index notation for whole-number powers and perform calculations involving integer exponents. | Introduction to index notation and powers is standard in Year 8. | Direct match |
| 2 | Exponent laws | 9 | Number and Algebra | Apply laws of exponents (product, quotient, power of a power) for integer exponents in algebraic and numeric contexts. | Formal use of index laws and algebraic manipulation is typically developed by Year 9. | Direct match |
| 2 | Zero as an exponent | 10 | Number and Algebra | Explain and use 0 as an exponent (a^0 = 1) within integer-index rules and expressions. | Zero exponent is generally consolidated with index laws at Years 9–10. | Direct match |
| 2 | Negative exponents | 10 | Number and Algebra | Interpret and manipulate negative integer exponents (reciprocal representation) and use them in calculations. | Negative exponents and reciprocal interpretation are Year 10 content in ACARA-style progression. | Direct match |
| 3 | Multiples and divisibility | 8 | Number and Algebra | Use divisibility rules and properties of multiples to solve problems, including factor and multiple reasoning. | Divisibility and factors/multiples are typical Year 8 content. | Direct match |
| 3 | Primes, composites, and prime factorization | 8 | Number and Algebra | Identify prime and composite numbers and represent integers as products of primes via prime factorisation. | Prime factorisation is standard in Years 7–8. | Direct match |
| 3 | Fundamental Theorem of Arithmetic | 8 | Number and Algebra | Understand uniqueness of prime factorisation and use it to reason about integers and factors. | Uniqueness of prime factorisation is the formalisation of prime-factor work usually covered by Year 8. | Direct match |
| 3 | Least common multiple (LCM) and greatest common divisor (GCD) | 8 | Number and Algebra | Determine and use LCM and GCD via prime factors to solve problems involving common multiples and factors. | LCM/GCD via prime factorisation is typical Year 8 material. | Direct match |
| 4 | Rigorous definition of fractions | 7 | Number and Algebra | Explain fractions as numbers that represent parts of a whole and points on the number line, and relate improper fractions and mixed numbers. | Foundational fraction concepts are core Year 7 content. | Direct match |
| 4 | Arithmetic with fractions and mixed numbers | 7 | Number and Algebra | Add, subtract, multiply and divide fractions and mixed numbers, including using common denominators and simplification. | Fraction operations are central Year 7–8 topics. | Direct match |
| 4 | Fraction comparison and simplification | 7 | Number and Algebra | Compare and order fractions, simplify fractions and convert between improper and mixed forms. | Comparison and simplification are standard Year 7 skills. | Direct match |
| 4 | Challenging word problems with fractions | 8 | Number and Algebra | Solve multi-step problems involving fractional quantities in real contexts and model with equations or diagrams. | Applying fraction operations to complex word problems typically extends across Years 7–8. | Partial match |
| 5 | Expressions and equations | 7 | Number and Algebra | Use algebraic expressions to represent situations and solve simple linear equations by balancing and standard manipulations. | Introduction to expressions and simple equations is Year 7–8 material. | Direct match |
| 5 | Linear equations | 9 | Number and Algebra | Solve linear equations with one variable, including rearrangement and solution strategies for integer and rational coefficients. | Systematic solution of linear equations is emphasised in Year 9. | Direct match |
| 5 | Applications of linear equations to word problems | 9 | Number and Algebra | Formulate and solve linear equations to model real-world problems and interpret solutions in context. | Modelling with linear equations is core Year 9 content; problem complexity may vary. | Direct match |
| 5 | Principles of inequalities | 9 | Number and Algebra | Understand inequality notation, compare values, and use algebraic rules to reason about inequalities. | Inequality notation and reasoning are introduced and developed by Year 9. | Direct match |
| 5 | Linear inequalities | 9 | Number and Algebra | Solve and graph linear inequalities and represent solution sets on number lines and in real contexts. | Solving simple linear inequalities is included in Years 9–10 curricula. | Direct match |
| 6 | Definition of decimal notation | 7 | Number and Algebra | Use decimal notation to represent fractional parts, locate decimal numbers on number lines and relate to place value. | Decimal place value and notation are Year 7 fundamentals. | Direct match |
| 6 | Rigorous exploration of arithmetic with decimals | 7 | Number and Algebra | Add, subtract, multiply and divide decimals accurately and apply to problem solving in context. | Decimal arithmetic and applications are Year 7–8 content. | Direct match |
| 6 | Decimal comparison and approximation | 7 | Number and Algebra | Compare and order decimals, round to given places and use approximations when appropriate. | Comparison and rounding of decimals are Year 7 skills. | Direct match |
| 6 | Conversion between fractions and decimals | 8 | Number and Algebra | Convert between fractions and decimals (including recurring decimals) and use conversions in calculations. | Conversion between representations is emphasised by Year 8. | Direct match |
| 6 | Rational numbers and their decimal representation | 8 | Number and Algebra | Represent rational numbers as decimals (terminating or recurring) and identify their properties. | Understanding rational number decimal forms is Year 8-level content. | Direct match |
| 7 | Definition of ratio and proportion | 7 | Number and Algebra | Use ratio language and notation and solve problems involving direct proportion of quantities. | Ratio and basic proportion are introduced in Year 7. | Direct match |
| 7 | Proportional thinking | 8 | Number and Algebra | Apply proportional reasoning to scale recipes, maps and similar contexts, recognising multiplicative relationships. | Proportional reasoning is a targeted Year 8 capability. | Direct match |
| 7 | Problem-solving with part-to-part and part-to-whole ratios | 7 | Number and Algebra | Solve problems involving comparisons of parts of a whole and allocations using ratios. | Ratios for part-to-part and part-to-whole are covered in lower secondary years. | Direct match |
| 7 | Variables in ratios and proportions | 9 | Number and Algebra | Express ratio relationships using variables and solve proportional equations algebraically. | Using algebra with ratios is typically introduced in Year 9 and links ratio to algebra. | Partial match |
| 7 | Unit conversion with conversion factors | 7 | Measurement and Geometry | Use unit conversion factors to convert between common metric units and solve measure problems. | Unit conversion and standard measures are Year 7–8 measurement content. | Direct match |
| 7 | Relationship between speed, distance, and time | 8 | Measurement and Geometry | Model and solve problems using the relation distance = speed × time and apply to real contexts. | Speed–distance–time problems are a classic Year 8 topic linking ratio and measurement. | Direct match |
| 7 | Joint work, relative speed, and average speed | 9 | Number and Algebra | Solve combined-rate and relative-speed problems, including work-rate and average-rate contexts. | Joint work and average-rate problems extend basic rate concepts and are usually Year 9 problem-solving topics. | Partial match |
| 8 | Definition of percent | 7 | Number and Algebra | Understand percent as a fraction of 100 and represent percentages in fraction and decimal form. | Percent concepts are introduced in Year 7. | Direct match |
| 8 | Relationships among percents, fractions, and decimals | 7 | Number and Algebra | Convert between percentages, fractions and decimals and use these relationships fluently. | Conversion among representations is core Year 7–8 work. | Direct match |
| 8 | Percents of numbers | 7 | Number and Algebra | Calculate percentages of quantities and solve routine percentage-of-number problems. | Finding percentages of quantities is Year 7–8 practice. | Direct match |
| 8 | Percent word problems | 8 | Number and Algebra | Solve multi-step percentage problems in financial and real-world contexts (discounts, tax, proportions). | Applied percent problems are included in Year 8 problem-solving. | Direct match |
| 8 | Percent increase and decrease | 8 | Number and Algebra | Calculate and interpret percentage change and apply compound percentage reasoning to simple cases. | Percentage change and applications are Year 8 content; compound cases may extend into Year 9. | Direct match |
| 9 | Definition of square root | 9 | Number and Algebra | Define square roots as inverse of squaring and represent them symbolically and numerically. | Square root concept is introduced by Year 9 as part of number and surds development. | Direct match |
| 9 | Equations with square roots | 9 | Number and Algebra | Solve simple equations involving square roots and check solutions in context. | Solving simple radical equations is aligned with Year 9 algebraic development. | Direct match |
| 9 | Non-integer square roots | 9 | Number and Algebra | Estimate and work with non-integer square roots, including decimal approximations and contextual interpretation. | Approximating irrational or non-integer roots is usually introduced in Year 9. | Partial match |
| 9 | Simplification of square roots | 10 | Number and Algebra | Simplify square roots using factorisation (surds), expressing results in simplest radical form. | Simplification of surds is a Year 10 objective in ACARA-style progression. | Direct match |
| 9 | Arithmetic with square roots | 10 | Number and Algebra | Perform arithmetic and algebraic operations with square roots (addition, multiplication, rationalisation where appropriate). | Manipulating surds and performing operations is typically Year 10 level. | Direct match |
| 10 | Angle measurement | 7 | Measurement and Geometry | Measure and classify angles in degrees, construct and interpret angle measures in problems. | Angle measurement and classification are Year 7 geometry fundamentals. | Direct match |
| 10 | Parallel lines | 8 | Measurement and Geometry | Use properties of parallel lines (alternate, corresponding angles) to reason about angle relationships. | Angle relationships with parallel lines are taught by Year 8. | Direct match |
| 10 | Angles in a triangle | 8 | Measurement and Geometry | Apply triangle-angle sum and use interior/exterior angle relationships to solve problems. | Triangle angle-sum and computation are Year 8 content. | Direct match |
| 10 | Angles in other polygons | 8 | Measurement and Geometry | Determine interior and exterior angle sums in polygons and use formulas for problem solving. | Angle-sum formulas and polygon angles are Year 8–9 topics. | Direct match |
| 11 | Segments and perimeter | 7 | Measurement and Geometry | Calculate perimeters of polygons and work with line segments and measurement units in geometric contexts. | Perimeter and segment measurement are Year 7 measurement basics. | Direct match |
| 11 | Triangle inequality | 9 | Measurement and Geometry | Apply and reason with the triangle inequality in geometric and measurement problems. | Triangle inequality is often treated as an extended geometric reasoning topic by Year 9. | Partial match |
| 11 | Triangle area | 8 | Measurement and Geometry | Calculate the area of triangles using base × height ÷ 2 and apply to composite shapes. | Triangle area formula and applications are Year 8 content. | Direct match |
| 11 | Circumference of a circle | 8 | Measurement and Geometry | Use the relationship between diameter and circumference (pi) and calculate circumference for given radii/diameters. | Circumference and circle measure links are Year 8 measurement topics. | Direct match |
| 11 | Area of a circle | 8 | Measurement and Geometry | Use A = πr^2 to calculate circle areas and apply to problems involving sectors and segments as appropriate. | Area of a circle and applications are Year 8 material. | Direct match |
| 11 | Unusual areas | 9 | Measurement and Geometry | Find areas of composite and non-standard regions using decomposition, transformation and algebraic reasoning. | Composite area problems require deeper reasoning usually developed in Year 9. | Partial match |
| 12 | The Pythagorean Theorem | 8 | Measurement and Geometry | Apply and prove the Pythagorean Theorem to solve problems involving right-angled triangles and distances. | Pythagoras is a central Year 8–9 geometry topic. | Direct match |
| 12 | Pythagorean triples | 9 | Number and Algebra / Geometry | Identify integer right-triangle side sets and use number-theoretic reasoning to generate and apply triples. | Triples combine number theory and geometry and are often extension material in Year 9. | Partial match |
| 12 | 30-60-90 and 45-45-90 triangles | 9 | Measurement and Geometry | Use properties of special right triangles to determine side ratios and solve geometry problems without full trigonometry. | Special triangle ratios are useful geometry knowledge introduced at Year 9; may exceed basic requirements. | Partial match |
| 12 | Types of quadrilaterals | 7 | Measurement and Geometry | Classify quadrilaterals by side, angle and symmetry properties and use these properties in reasoning. | Classification of quadrilaterals is Year 7–8 geometry content. | Direct match |
| 12 | Quadrilateral area | 8 | Measurement and Geometry | Calculate areas of common quadrilaterals (parallelogram, trapezium, rectangle) and apply decomposition methods. | Area of quadrilaterals and decomposition strategies belong to Year 8 measurement. | Direct match |
| 13 | Average (mean) | 7 | Statistics and Probability | Calculate and interpret the mean of a data set and use mean to describe centre in context. | Mean is a foundational Year 7 statistic concept. | Direct match |
| 13 | Averages as a balancing act | 8 | Statistics and Probability | Understand mean as a balancing point of data and use this idea to reason about distributions. | Conceptual understanding of averages is part of developing statistical literacy around Year 8. | Direct match |
| 13 | Median, mode, and range | 7 | Statistics and Probability | Determine and interpret median, mode and range for data sets and choose appropriate measures for context. | Median, mode and range are core Year 7 topics in statistics. | Direct match |
| 13 | Limits of basic statistics | 10 | Statistics and Probability | Discuss the limitations and potential for misinterpretation of simple statistics and graphical displays. | Critical interpretation and limitations of statistics are mature skills often emphasised by Year 10. | Partial match |
| 13 | Types of graphs and charts | 7 | Statistics and Probability | Create, interpret and compare bar charts, histograms, dot plots and other displays to represent data. | Representing and interpreting data visually is Year 7 content. | Direct match |
| 14 | Numbers in lists | 7 | Number and Algebra | Generate and analyse number lists and sequences, identifying patterns and rules to continue or generalise them. | Recognition of patterns in sequences is Year 7 material. | Direct match |
| 14 | Venn diagrams | 8 | Statistics and Probability / Number and Algebra | Use Venn diagrams to represent sets, intersections and unions and to solve counting problems. | Venn diagrams for sets and simple counting are Year 8 content. | Direct match |
| 14 | Multiplication principle | 9 | Number and Algebra | Use the counting principle to determine the number of outcomes of multi-stage experiments and combinatorial arrangements. | Formal multiplication principle is typically introduced by Year 9 as counting grows more systematic. | Partial match |
| 14 | Casework | 9 | Number and Algebra | Apply systematic case analysis to count possibilities, ensuring completeness without double counting. | Systematic casework is a problem-solving/combinatorics skill developed in middle-secondary years. | Partial match |
| 14 | Pairs | 9 | Number and Algebra | Count and reason about unordered and ordered pairs, using combinatorial reasoning and simple formulas. | Pair-counting introduces combinatorics and is usually a Year 9 extension of counting ideas. | Partial match |
| 14 | Introduction to probability | 7 | Statistics and Probability | Introduce basic probability concepts, sample spaces, simple event probabilities and relative frequency interpretation. | Basic probability and relative frequency are Year 7–8 content. | Direct match |
| 15 | Find a pattern | 7-10 | General capabilities / Number and Algebra | Identify and generalise patterns and use them to form conjectures and guide problem-solving strategies across contexts. | Pattern recognition and generalisation are cross-year problem-solving proficiencies in the ACARA progression. | Direct match |
| 15 | Make a list | 7-10 | General capabilities / Number and Algebra | Use systematic lists and organised tables to explore possibilities and reduce complexity in problem solving. | Making lists is a standard heuristic taught across Years 7–10 under problem solving. | Direct match |
| 15 | Draw a picture | 7-10 | General capabilities / Measurement and Geometry | Use diagrams, sketches and visual models to represent problems, clarify structure and guide solution strategies. | Visual modelling is a core problem-solving technique emphasised across the middle years. | Direct match |
| 15 | Work backwards | 7-10 | General capabilities / Number and Algebra | Apply backwards reasoning and reverse-engineering of problems to construct solutions and verify results. | Working backwards is a general problem-solving method taught and used across Years 7–10. | Direct match |
Notes for printing / Excel import:
- Copy the HTML table into a file saved as .html and open in a browser; use Print > Save as PDF or select and paste into Excel (most spreadsheet apps will parse the table into cells).
- Each row corresponds to one chapter subtopic; modify the Year or Match level where your local scope differs from the ACARA progression.
- Match-level key: 'Direct match' = closely aligned to typical ACARA Year descriptor; 'Partial match' = overlaps but may be more advanced or focused on problem solving; 'Extension / exceeds year expectations' = goes beyond the usual Year-level scope. (No rows were labelled 'Extension' as most Prealgebra content maps within Years 7–10.)