Australia · ACARA Content Descriptions
Foundation Mathematics
A comprehensive introduction to mathematical thinking designed for the first year of school. Students develop a sense of number, spatial reasoning, and logical patterns through hands on exploration and collaborative problem solving.
01Counting Objects to 10
Students explore the concept of quantity and the relationship between numbers and physical objects.
Students review whole numbers, their place value up to billions, and how to read and write large numbers.
Students extend their understanding of numbers to include rational numbers, representing them as fractions.
Students extend their understanding of numbers to include rational numbers, representing them as decimals.
Students extend their understanding of numbers to include rational numbers, representing them as percentages.
Students perform addition and subtraction with positive and negative integers, understanding the rules for each operation.
Students perform multiplication and division with positive and negative integers, understanding the rules for each operation.
Students identify prime and composite numbers and understand their properties, including prime factorisation.
Students explore factors and multiples, and apply divisibility rules to efficiently determine factors of numbers.
Students identify equivalent fractions and compare and order fractions with different denominators.
Students perform addition and subtraction of fractions, including mixed numbers, with like and unlike denominators.
02Copying and Continuing Repeating Patterns
Students identify, describe, and create patterns to build a foundation for algebraic reasoning.
Students apply the order of operations (BODMAS/PEMDAS) to evaluate numerical expressions involving multiple operations.
Students understand variables, terms, and coefficients, and write simple algebraic expressions from word descriptions.
Students combine like terms to simplify algebraic expressions, applying the commutative and associative properties.
Students solve linear equations involving one variable using inverse operations.
Students solve linear equations involving two operations, applying the order of inverse operations correctly.
Students understand and graph simple linear inequalities, using appropriate symbols and notation.
Students identify linear relationships, create tables of values, and describe patterns in linear sequences.
Students plot points from tables of values to graph linear relationships on a Cartesian plane.
Students understand and use the Cartesian coordinate system to locate and plot points in all four quadrants.
Students explore input-output tables to identify rules for simple linear functions, conceptualising them as 'function machines'.
03Naming and Recognising 2D Shapes
Students investigate the properties of two dimensional shapes and three dimensional objects in their environment.
Students classify polygons based on their properties, including number of sides, angles, and regularity.
Students investigate and compare the properties of various quadrilaterals (e.g., squares, rectangles, parallelograms, trapezoids).
Students classify triangles based on their side lengths and angle measures (e.g., equilateral, isosceles, scalene, right, acute, obtuse).
Students identify and measure different types of angles (acute, obtuse, right, straight, reflex) using a protractor.
Students identify and calculate complementary and supplementary angles, and angles at a point or on a straight line.
Students identify and calculate vertically opposite angles and angles formed by parallel lines and a transversal.
Students perform and describe translations of 2D shapes on a Cartesian plane.
Students perform and describe reflections of 2D shapes across a line on a Cartesian plane.
Students perform and describe rotations of 2D shapes around a point on a Cartesian plane.
Students identify and create shapes with line symmetry and rotational symmetry, determining the order of rotational symmetry.
04Comparing Length: Longer and Shorter
Students use direct comparison to explore length, mass, and capacity using informal units.
Students understand and apply the concept of congruence to 2D shapes, identifying congruent figures.
Students understand and apply the concept of similarity to 2D shapes, identifying similar figures and scale factors.
Students are introduced to the Pythagorean theorem and apply it to find unknown side lengths in right-angled triangles.
Students apply their knowledge of shapes, angles, and transformations to solve multi-step geometric problems.
Students calculate the perimeter of various polygons, including irregular shapes, using appropriate units.
Students calculate the area of rectangles and triangles using formulas and appropriate square units.
Students derive and apply formulas to calculate the area of parallelograms and trapezoids.
Students understand the concept of circumference and calculate it using the formula involving pi.
Students derive and apply the formula to calculate the area of circles.
Students calculate the volume of rectangular and triangular prisms using formulas and cubic units.
05Daily Routines and Sequences of Events
Students develop an awareness of the passage of time and the sequence of daily occurrences.
Students understand the relationship between speed, distance, and time and solve related problems.
Students compare and convert between Celsius and Fahrenheit temperature scales.
Students create simple budgets, record financial transactions, and understand concepts of income and expenditure.
Students calculate simple interest and apply it to real-world financial scenarios like savings and loans.
Students compare prices and use unit pricing to determine the best value for money in consumer situations.
Students are introduced to different types of income and the basic concept of taxation.
Students learn to express very large and very small numbers using scientific notation and perform basic operations.
Students calculate the volume of cylinders using formulas and cubic units.
Students calculate the surface area of cylinders by finding the area of its circular bases and curved surface.
Students calculate the volume and surface area of objects made from combining two or more simple 3D shapes.
06Sorting Objects into Groups
Students collect information to answer questions and explore the likelihood of everyday events.
Students design and conduct surveys, collect data, and organise it into frequency tables and grouped frequency tables.
Students construct and interpret column graphs and dot plots to represent discrete data.
Students construct and interpret histograms and stem-and-leaf plots to represent continuous data.
Students calculate and interpret the mean, median, and mode for various datasets.
Students calculate and interpret the range of a dataset as a measure of spread.
Students critically interpret various data displays, identifying trends, patterns, and potential misrepresentations.
Students differentiate between theoretical and experimental probability and calculate probabilities of simple events.
Students identify the sample space for simple chance experiments and list all possible outcomes.
Students understand and calculate the probability of complementary events.