Below is a single table formatted in HTML so you can copy-paste into Excel (or save as an HTML file and open in Excel). Columns: Chapter, Subtopic, Year, Strand, ACARA-style content wording, One-line justification, Match level.
| Chapter | Subtopic | Year | Strand | ACARA-style content wording | One-line justification | Match level |
|---|---|---|---|---|---|---|
| 1 Properties of Arithmetic | Rigorous definition of arithmetic basics | Year 7 | Number and Algebra | Apply and explain properties of operations for integers and rational numbers to calculate and justify results | Introduces formal operation properties used in Year 7 computational fluency. | Direct match |
| 1 Properties of Arithmetic | Clever applications of arithmetic rules to simplify calculations | Year 7 | Number and Algebra | Use arithmetic properties and strategies to perform efficient calculations and solve problems | Focuses on computational strategies consistent with Year 7 problem solving with numbers. | Direct match |
| 2 Exponents | Exponentiation and powers | Year 8 | Number and Algebra | Use index notation for integer powers and represent whole-number powers of integers and fractions | Covers introduction to powers and notation typical of Year 8. | Direct match |
| 2 Exponents | Exponent laws | Year 9 | Number and Algebra | Apply laws of exponents for multiplication, division and power of a power with integer exponents | Develops index laws that align to Year 9 content on the laws of exponents. | Direct match |
| 2 Exponents | Zero as an exponent | Year 9 | Number and Algebra | Explain and apply the zero index rule in computations and simplifications | Explains the zero exponent rule within index-law treatment. | Direct match |
| 2 Exponents | Negative exponents | Year 10 | Number and Algebra | Use negative integer exponents to represent reciprocals and perform simplifications | Negative exponents and reciprocal interpretation extend Year 9 work into Year 10. | Partial match |
| 3 Number Theory | Multiples and divisibility | Year 7 | Number and Algebra | Investigate and use divisibility rules and properties of multiples in problem solving | Basic divisibility and multiples are core Year 7 number concepts. | Direct match |
| 3 Number Theory | Primes, composites, and prime factorization | Year 8 | Number and Algebra | Identify primes and composites and use prime factorisation to solve problems | Prime factorisation and classification usually taught in Year 8. | Direct match |
| 3 Number Theory | Fundamental Theorem of Arithmetic | Year 9 | Number and Algebra | Use unique prime factorisation to justify properties of numbers and solve problems | Formal statement and use of uniqueness goes slightly beyond basic Year 8 factorisation. | Partial match |
| 3 Number Theory | Least common multiple (LCM) and greatest common divisor (GCD) | Year 8 | Number and Algebra | Find LCM and GCD using prime factorisation and use them to solve problems | Computing LCM/GCD aligns with Year 8 number strategies. | Direct match |
| 4 Fractions | Rigorous definition of fractions | Year 7 | Number and Algebra | Understand fractions as numbers representing parts of a whole and as quotients | Formalising fraction meaning is a Year 7 core descriptor. | Direct match |
| 4 Fractions | Arithmetic with fractions and mixed numbers | Year 7 | Number and Algebra | Add, subtract, multiply and divide with fractions and mixed numbers in calculation and problem contexts | Standard Year 7 operations on fractions and mixed numbers. | Direct match |
| 4 Fractions | Fraction comparison and simplification | Year 7 | Number and Algebra | Compare and order fractions, simplify to lowest terms and convert between improper fractions and mixed numbers | Comparison and simplification are fundamental Year 7 skills. | Direct match |
| 4 Fractions | Challenging word problems with fractions | Year 8 | Number and Algebra | Solve multi-step problems involving fractions using reasoning and algebraic representation where appropriate | Application to complex word problems extends routine Year 7 tasks into problem solving. | Partial match |
| 5 Equations and Inequalities | Expressions and equations | Year 7 | Number and Algebra | Use algebraic notation to represent relationships and evaluate expressions for given values | Introduction to algebraic notation and simple expressions is Year 7 content. | Direct match |
| 5 Equations and Inequalities | Linear equations | Year 8 | Number and Algebra | Solve simple linear equations using properties of equality and apply to problems | Solving one-step and two-step linear equations is Year 8 material. | Direct match |
| 5 Equations and Inequalities | Applications of linear equations to word problems | Year 8 | Number and Algebra | Model real-life situations with linear equations and solve problems using algebraic methods | Translating contexts into equations matches Year 8 problem-solving emphasis. | Direct match |
| 5 Equations and Inequalities | Principles of inequalities | Year 9 | Number and Algebra | Understand inequality notation and apply rules when manipulating inequalities | Formal manipulation and reasoning about inequalities are taught in Year 9. | Direct match |
| 5 Equations and Inequalities | Linear inequalities | Year 9 | Number and Algebra | Solve linear inequalities and represent solution sets on number lines | Solve and graph linear inequalities is standard Year 9 content. | Direct match |
| 6 Decimals | Definition of decimal notation | Year 7 | Number and Algebra | Understand decimal notation and place value for decimals and use them in calculations | Place-value and meaning of decimals are Year 7 fundamentals. | Direct match |
| 6 Decimals | Rigorous exploration of arithmetic with decimals | Year 7 | Number and Algebra | Add, subtract, multiply and divide decimals, explaining strategies and error checking | Decimal arithmetic practice aligns to Year 7 operations outcomes. | Direct match |
| 6 Decimals | Decimal comparison and approximation | Year 7 | Number and Algebra | Compare and round decimals and use estimation to judge reasonableness of answers | Comparing and rounding decimals is part of Year 7 numeracy skills. | Direct match |
| 6 Decimals | Conversion between fractions and decimals | Year 8 | Number and Algebra | Convert between fractions, decimals and percentages and use equivalences in calculations | Conversion tasks are explicitly covered in Year 8-9; basic conversions are Year 8. | Direct match |
| 6 Decimals | Rational numbers and their decimal representation | Year 9 | Number and Algebra | Recognise rational numbers and explain repeating and terminating decimal representations | Explaining rational decimal forms and repeating patterns fits Year 9 descriptors. | Direct match |
| 7 Ratios, Conversions, and Rates | Definition of ratio and proportion | Year 7 | Number and Algebra | Use ratio notation and reason about part-to-part and part-to-whole relationships | Introductory ratio concepts are core Year 7 content. | Direct match |
| 7 Ratios, Conversions, and Rates | Proportional thinking | Year 8 | Number and Algebra | Recognise and solve proportional relationships using tables, graphs and equations | Proportional reasoning and representation are Year 8 focuses. | Direct match |
| 7 Ratios, Conversions, and Rates | Problem-solving with part-to-part and part-to-whole ratios | Year 8 | Number and Algebra | Solve problems involving mixtures, scales and maps using ratio reasoning | Application of ratio concepts to contexts is Year 8 problem solving. | Direct match |
| 7 Ratios, Conversions, and Rates | Variables in ratios and proportions | Year 9 | Number and Algebra | Use algebraic symbols to represent proportional relationships and solve for unknowns | Introducing variables into ratio relationships extends Year 8 to Year 9 algebraic form. | Partial match |
| 7 Ratios, Conversions, and Rates | Unit conversion with conversion factors | Year 7 | Measurement and Geometry | Use and convert between units of measurement using appropriate conversion factors | Unit conversion is part of Year 7 measurement outcomes. | Direct match |
| 7 Ratios, Conversions, and Rates | Relationship between speed, distance, and time | Year 8 | Measurement and Geometry | Use rate structure to connect distance, time and speed and solve related problems | Speed-distance-time problems align to Year 8 rate and measurement tasks. | Direct match |
| 7 Ratios, Conversions, and Rates | Joint work, relative speed, and average speed | Year 9 | Number and Algebra | Apply combined work and average-rate models in multi-step problems | Combined-rate and more advanced average speed problems extend curriculum expectations. | Extension / exceeds year expectations |
| 8 Percents | Definition of percent | Year 7 | Number and Algebra | Understand percent as a fraction of 100 and relate to fractions and decimals | Basic percent meaning and conversion are Year 7 content. | Direct match |
| 8 Percents | Relationships among percents, fractions, and decimals | Year 8 | Number and Algebra | Convert between percentages, fractions and decimals and use equivalences in problem solving | Conversions and equivalences are Year 8 focuses. | Direct match |
| 8 Percents | Percents of numbers | Year 7 | Number and Algebra | Calculate percentages of quantities and apply to discount and basic financial contexts | Computing percent of a quantity is a standard Year 7-8 skill. | Direct match |
| 8 Percents | Percent word problems | Year 8 | Number and Algebra | Solve multi-step percentage problems including increases, decreases and reverse percentage | Applied percent problem solving is Year 8 material. | Direct match |
| 8 Percents | Percent increase and decrease | Year 8 | Number and Algebra | Calculate percent change and apply to contexts such as growth and decay | Percent change calculations map to Year 8 outcomes. | Direct match |
| 9 Square Roots | Definition of square root | Year 9 | Number and Algebra | Define square roots and relate them to inverse operations of squaring | Introduction to roots and inverse operations aligns to Year 9. | Direct match |
| 9 Square Roots | Equations with square roots | Year 10 | Number and Algebra | Solve simple equations involving square roots and squares, including checking solutions | Solving equations with radicals often appears in Year 10 algebra. | Direct match |
| 9 Square Roots | Non-integer square roots | Year 10 | Number and Algebra | Approximate irrational square roots and use a calculator appropriately in problem solving | Approximating non-integer roots and irrational numbers is a Year 10 skill set. | Direct match |
| 9 Square Roots | Simplification of square roots | Year 10 | Number and Algebra | Simplify square roots using factorisation and express in simplest surd form | Simplifying radicals via factorisation aligns to Year 10 algebra topics. | Direct match |
| 9 Square Roots | Arithmetic with square roots | Year 10 | Number and Algebra | Add, subtract, multiply and divide expressions containing square roots, applying simplification rules | Algebraic manipulation of surds is a Year 10 expectation. | Direct match |
| 10 Angles | Angle measurement | Year 7 | Measurement and Geometry | Measure and construct angles and use degree and angle notation in geometric contexts | Basic angle measurement is a Year 7 geometry outcome. | Direct match |
| 10 Angles | Parallel lines | Year 8 | Measurement and Geometry | Identify and use angle relationships formed by parallel lines and a transversal | Parallel-lines angle rules are typically taught in Year 8. | Direct match |
| 10 Angles | Angles in a triangle | Year 7 | Measurement and Geometry | Use angle sum properties of triangles to solve for unknown angles | Triangle angle-sum and basic interior/exterior angle relationships are Year 7 content. | Direct match |
| 10 Angles | Angles in other polygons | Year 8 | Measurement and Geometry | Investigate angle sums and use them to find interior and exterior angles of polygons | Extends triangle angle work to polygons as in Year 8. | Direct match |
| 11 Perimeter and Area | Segments and perimeter | Year 7 | Measurement and Geometry | Calculate perimeters of simple and composite shapes using appropriate units | Perimeter calculation is a core Year 7 measurement skill. | Direct match |
| 11 Perimeter and Area | Triangle inequality | Year 9 | Measurement and Geometry | Investigate and apply triangle inequality to determine possible side lengths and problem contexts | Triangle inequality is a deeper geometric property usually covered later. | Partial match |
| 11 Perimeter and Area | Triangle area | Year 7 | Measurement and Geometry | Calculate area of triangles using appropriate formulas and apply to problems | Triangle area formulas and applications are Year 7-8 content. | Direct match |
| 11 Perimeter and Area | Circumference of a circle | Year 8 | Measurement and Geometry | Use and apply the relationship between radius, diameter and circumference of circles | Circumference and basic circle measures are Year 8 measurement topics. | Direct match |
| 11 Perimeter and Area | Area of a circle | Year 8 | Measurement and Geometry | Apply the formula for the area of a circle and solve related problems | Area of a circle and related problems fall into Year 8 measurement. | Direct match |
| 11 Perimeter and Area | Unusual areas | Year 9 | Measurement and Geometry | Find areas of composite and non-standard shapes using dissection and algebraic methods | Non-standard and composite area problems expand on Year 8 basics into Year 9 problem solving. | Partial match |
| 12 Right Triangles and Quadrilaterals | The Pythagorean Theorem | Year 8 | Measurement and Geometry | Use the Pythagorean theorem to find unknown sides in right-angled triangles and solve problems | Pythagoras is taught in Year 8 as a fundamental geometry result. | Direct match |
| 12 Right Triangles and Quadrilaterals | Pythagorean triples | Year 9 | Number and Algebra / Measurement and Geometry | Use integer Pythagorean triples to generate examples and solve integer-length problems | Exploration of integer triples is an extension beyond the basic Year 8 theorem. | Extension / exceeds year expectations |
| 12 Right Triangles and Quadrilaterals | 30-60-90 and 45-45-90 triangles | Year 9 | Measurement and Geometry | Recognise and use properties of special right triangles to determine side ratios | Special triangle ratios are usually introduced in Year 9 geometry/trigonometry foundations. | Direct match |
| 12 Right Triangles and Quadrilaterals | Types of quadrilaterals | Year 7 | Measurement and Geometry | Classify quadrilaterals by their properties and relationships | Identification and classification of quadrilaterals is Year 7 content. | Direct match |
| 12 Right Triangles and Quadrilaterals | Quadrilateral area | Year 8 | Measurement and Geometry | Calculate areas of common quadrilaterals using decomposition and formulae | Area calculations for quadrilaterals extend Year 7 perimeter and Year 8 area work. | Direct match |
| 13 Data and Statistics | Average (mean) | Year 7 | Statistics and Probability | Calculate and interpret the mean for sets of data and use it to describe data | Mean as a measure of centre is introduced in Year 7 statistics. | Direct match |
| 13 Data and Statistics | Averages as a balancing act | Year 8 | Statistics and Probability | Interpret mean as a balancing point and use this idea to solve data problems | Conceptual interpretation of mean as balancing is often developed in Year 8. | Partial match |
| 13 Data and Statistics | Median, mode, and range | Year 7 | Statistics and Probability | Calculate and compare median, mode and range and discuss suitability as measures of centre and spread | Basic descriptive statistics are Year 7 core content. | Direct match |
| 13 Data and Statistics | Limits of basic statistics | Year 9 | Statistics and Probability | Investigate how mean, median and mode can be affected by outliers and describe limitations | Critical evaluation of statistical measures is more advanced, typically Year 9. | Partial match |
| 13 Data and Statistics | Types of graphs and charts | Year 7 | Statistics and Probability | Construct and interpret column graphs, dot plots and simple histograms to represent data | Constructing and reading basic graphs is Year 7 material. | Direct match |
| 13 Data and Statistics | Working with data in problem contexts | Year 8 | Statistics and Probability | Use statistical displays and summary measures to make inferences in context | Applying data skills to contexts continues across Years 7-8. | Direct match |
| 14 Counting | Numbers in lists | Year 9 | Number and Algebra | Use sequences and indexing to organise counting tasks and reason about enumerations | Organising lists and sequences is often formalised in Year 9 counting contexts. | Partial match |
| 14 Counting | Venn diagrams | Year 9 | Statistics and Probability / Number and Algebra | Use Venn diagrams to represent sets and count elements in unions, intersections and complements | Venn-diagram counting and set reasoning are Year 9 topics in combinatorics and probability. | Direct match |
| 14 Counting | Multiplication principle | Year 9 | Number and Algebra | Apply the fundamental counting principle to calculate numbers of outcomes for sequential choices | Multiplication principle for counting appears in Year 9 combinatorics. | Direct match |
| 14 Counting | Casework | Year 9 | Number and Algebra | Use systematic case analysis to enumerate possibilities and avoid double counting | Casework as a counting strategy is standard in Year 9 problem solving. | Direct match |
| 14 Counting | Pairs | Year 9 | Number and Algebra | Count pairings and matchings using combinatorial reasoning | Pair-counting and simple combinations are Year 9 combinatorics. | Direct match |
| 14 Counting | Introduction to probability | Year 8 | Statistics and Probability | Determine probability of simple events using equally likely outcomes and counting methods | Introductory probability is Year 8 content; counting supports probability calculations. | Direct match |
| 15 Problem-Solving Strategies | Find a pattern | Years 7-10 | General capability - Problem solving / Number and Algebra | Use pattern recognition and algebraic reasoning to conjecture and test general rules | Pattern-finding is a cross-year problem-solving skill integrated across the curriculum. | Direct match |
| 15 Problem-Solving Strategies | Make a list | Years 7-10 | General capability - Problem solving / Number and Algebra | Use organised lists to systematically explore possibilities and solve counting problems | Making lists is a general strategy emphasised across year levels for problem solving. | Direct match |
| 15 Problem-Solving Strategies | Draw a picture | Years 7-10 | General capability - Problem solving / Measurement and Geometry | Use diagrams, graphs and models to represent and reason about mathematical situations | Diagramming is a widely taught strategy across Years 7-10 for reasoning and modelling. | Direct match |
| 15 Problem-Solving Strategies | Work backwards | Years 7-10 | General capability - Problem solving / Number and Algebra | Apply backwards reasoning to solve problems by reversing steps from the desired result | Working backwards is a standard strategy taught through Years 7-10 to develop reasoning. | Direct match |
Notes on use:
- Years are assigned to where each subtopic most directly aligns in the Australian Curriculum (ACARA) Years 7-10 progression; many topics span multiple years, so where appropriate a higher year was chosen if the subtopic requires more formalism (marked Partial or Extension where content goes beyond typical expectations).
- Strands used are the main ACARA strands: Number and Algebra, Measurement and Geometry, Statistics and Probability, and General capability outcome for problem-solving strategies where the topic is cross-curricular.
- To paste into Excel: copy the whole table HTML into a text file with .html extension and open in Excel, or paste the table rows into Excel using 'Paste Special - HTML'.
Citation: Prealgebra Text, Richard Rusczyk, David Patrick, Ravi Boppana, ISBN 978-1-934124-21-5 (mapping based on chapter topics and typical ACARA progression Years 7-10).