The Australian Curriculum, set by the Australian Curriculum, Assessment and Reporting Authority (ACARA), structures primary school numeracy across three key strands:

Number and Algebra, Measurement and Geometry, and Statistics and Probability.

These strands are further broken down into a detailed National Numeracy Learning Progression, which helps teachers track student development across 14 sub-elements. Here's a section-by-section guide to the numeracy topics covered from Grade 1 to Grade 7.

Part 1: Number Sense and Algebra

This is the largest element and focuses on understanding numbers, operations, patterns, and financial literacy.

Number and Place Value

Years 1-2: Students develop confidence with numbers up to 100 and beyond. They learn to skip count by twos, fives, and tens, and model, read, and write numbers to at least four digits by the end of Year 2.

Years 3-4: The focus shifts to numbers up to tens of thousands. Students explore place value, apply it to simple calculations, and round numbers to estimate solutions.

Years 5-7: Students extend their understanding to millions and work with integers (positive and negative numbers). They solve complex problems involving large numbers and use efficient mental and written strategies.

Fractions, Decimals, and Percentages

Years 1-2: Students are introduced to halves and quarters as visual representations of part-whole relationships.

Years 3-4: They begin to model and represent common fractions (thirds, fifths, etc.) and decimals (tenths, hundredths), understanding them as numbers that sit between whole numbers.

Years 5-7: Students connect fractions, decimals, and percentages and perform simple conversions between them. They multiply and divide fractions and decimals, and use percentages to calculate discounts or compare quantities.

Additive and Multiplicative Strategies

Years 1-2: Students use counting strategies to solve addition and subtraction problems. They begin to visualize numbers and count on or back to find totals, moving from using objects to mental strategies.

Years 3-4: Students start thinking multiplicatively, using repeated addition to represent multiplication. They solve division problems through equal sharing and grouping.

Years 5-7: Students develop fluency with multiplication and division of larger numbers. They solve multi-step problems and use order of operations (BODMAS) in contextualized situations.

Money and Financial Mathematics

Years 1-2: Students identify situations involving money and learn to recognize coins and notes. They practice using combinations of coins for simple purchases.

Years 3-4: Students apply their knowledge of the value of money to simple purchasing and budgeting scenarios.

Years 5-7: Financial numeracy deepens as students justify the use of money, calculate costs, and develop skills for making informed financial decisions.

Patterns and Algebra

Years 1-2: Students recognize repeating patterns in the environment and use them for prediction.

Years 3-4: They describe and continue growing number patterns and begin to understand how patterns relate to algebraic thinking.

Years 5-7: Students create algebraic expressions and evaluate them by substituting values. They solve simple linear equations and plot coordinates on the Cartesian plane, learning to use pronumerals and formulas.

Part 2: Measurement and Geometry

This element covers spatial reasoning, measurement concepts, and geometric properties.

Understanding Units of Measurement

Years 1-2: Students use informal units to measure length, mass, and capacity. They compare and order objects based on these attributes.

Years 3-4: Formal units (centimetres, grams, litres) are introduced. Students calculate perimeters of shapes and begin calculating areas using grid methods.

Years 5-7: Formulas for area and volume are established (e.g., Area = length × width). Students calculate volumes of rectangular prisms, solve problems involving surface area, and use measurement in design contexts.

Shape and Geometric Reasoning

Years 1-2: Students identify and describe 2D shapes (circles, squares, triangles) and 3D objects (spheres, cubes, cylinders) in the environment.

Years 3-4: They draw different views of prisms and structures, developing spatial visualization skills.

Years 5-7: Students classify angles (complementary, supplementary, vertically opposite) and investigate parallel lines. They describe transformations on the Cartesian plane (translations, reflections, rotations of multiples of 90°).

Location and Transformation

Years 1-2: Students describe position using simple language (left, right, above, below) and follow directions.

Years 3-4: They use simple maps and grids, understanding coordinates and directions.

Years 5-7: Students extend to the Cartesian plane, using coordinates to describe transformations. They create and analyze patterns using combinations of reflections and rotations.

Measuring Time

Years 1-2: Students connect days of the week to events and tell time on analog clocks to the hour and half-hour.

Years 3-4: They read analog and digital times to the minute and calculate simple time durations.

Years 5-7: Students use timelines (including those with negative numbers for historical dates) and convert between units of time.

Part 3: Statistics and Probability

This element helps students understand data and the concept of chance.

Data Representation and Interpretation

Years 1-2: Students collect simple data (e.g., favorite color) and represent it using picture graphs and simple tables.

Years 3-4: They construct column graphs and interpret information from data displays to answer questions.

Years 5-7: Students explore more complex data displays, including stem-and-leaf plots and dot plots. They investigate issues using numerical data from primary and secondary sources, and learn to choose the most appropriate graph type.

Understanding Chance

Years 1-2: Students identify and describe possible events as "likely" or "unlikely" using everyday language.

Years 3-4: They conduct simple chance experiments and list possible outcomes.

Years 5-7: Students quantify chance using fractions, decimals, and percentages. They make predictions based on data and understand that some events are more likely than others.

Helping Students Across All Areas

The ACARA numeracy progression is designed so teachers can identify where each student is and what they need to learn next. A student might be at different levels across different sub-elements, and that's completely normal.

Key skills like estimation and calculating are embedded across all areas—students are encouraged to estimate solutions before calculating and to use digital technologies and mental strategies appropriately. The progression is also linked across learning areas like Science, Geography, and HASS, where students apply numeracy to interpret data, construct maps, and understand financial concepts in real-world contexts.