Mathematics K–10 (2022)

demonstrates an understanding of how whole numbers indicate quantity

reads numerals and represents whole numbers to at least 20

sorts, describes, names and makes two-dimensional shapes, including triangles, circles, squares and rectangles

describes and compares areas of similar shapes

reasons about number relations to model addition and subtraction by combining and separating, and comparing collections

represents the relations between the parts that form the whole, with numbers up to 10

describes and compares the masses of objects

sequences events and reads hour time on clocks

recognises, describes and continues repeating patterns

forms equal groups by sharing and counting collections of objects

manipulates, describes and sorts three-dimensional objects

describes and compares volumes

describes position and gives and follows simple directions

describes and compares lengths

identifies half the length and the halfway point

contributes to collecting data and interprets data displays made from objects

recognises language that represents number

responds to and uses language that represents number

counts in everyday contexts

represents number in everyday contexts

compares and orders numbers

demonstrates knowledge of fractions in everyday contexts

demonstrates knowledge of decimals and percentages in everyday contexts

uses strategies for addition and subtraction

uses strategies for multiplication and division

demonstrates knowledge of money in everyday contexts

plans and manages personal finances

recognises and applies patterns in everyday contexts

demonstrates knowledge of time in everyday contexts

organises and measures time in everyday contexts

measures and uses length in everyday contexts

measures and uses volume, capacity and mass in everyday contexts

measures and uses area in everyday contexts

explores 2-dimensional shapes and 3-dimensional objects

demonstrates knowledge of position and direction in everyday contexts

recognises and represents data in everyday contexts

interprets information from data displays

applies chance and probability to everyday events

measures, records, compares and estimates the masses of objects using uniform informal units

describes, compares and orders durations of events, and reads half- and quarter-hour time

recognises and describes the element of chance in everyday events

applies an understanding of place value and the role of zero to read, write and order two- and three-digit numbers

reasons about representations of whole numbers to 1000, partitioning numbers to use and record quantity values

uses the structure of equal groups to solve multiplication problems, and shares or groups to solve division problems

measures, records, compares and estimates the masses of objects using uniform informal units

describes, compares and orders durations of events, and reads half- and quarter-hour time

represents and describes the positions of objects in familiar locations

measures, records, compares and estimates lengths and distances using uniform informal units, as well as metres and centimetres

creates and recognises halves, quarters and eighths as part measures of a whole length

recognises, describes and represents familiar three-dimensional objects

measures, records, compares and estimates internal volumes (capacities) and volumes using uniform informal units

recognises, describes and represents familiar three-dimensional objects

measures, records, compares and estimates internal volumes (capacities) and volumes using uniform informal units

uses number bonds and the relationship between addition and subtraction to solve problems involving partitioning

uses number bonds and the relationship between addition and subtraction to solve problems involving partitioning

recognises and describes the element of chance in everyday events

recognises, describes and represents shapes including quadrilaterals and other common polygons

measures and compares areas using uniform informal units in rows and columns

represents and describes the positions of objects in familiar locations

measures, records, compares and estimates lengths and distances using uniform informal units, as well as metres and centimetres

creates and recognises halves, quarters and eighths as part measures of a whole length

recognises, describes and represents shapes including quadrilaterals and other common polygons

measures and compares areas using uniform informal units in rows and columns

uses the structure of equal groups to solve multiplication problems, and shares or groups to solve division problems

applies an understanding of place value and the role of zero to read, write and order two- and three-digit numbers

reasons about representations of whole numbers to 1000, partitioning numbers to use and record quantity values

gathers and organises data, displays data in lists, tables and picture graphs

reasons about representations of data to describe and interpret the results

gathers and organises data, displays data in lists, tables and picture graphs

reasons about representations of data to describe and interpret the results

recognises language that represents number

responds to and uses language that represents number

counts in everyday contexts

represents number in everyday contexts

compares and orders numbers

demonstrates knowledge of fractions in everyday contexts

demonstrates knowledge of decimals and percentages in everyday contexts

uses strategies for addition and subtraction

uses strategies for multiplication and division

demonstrates knowledge of money in everyday contexts

plans and manages personal finances

recognises and applies patterns in everyday contexts

demonstrates knowledge of time in everyday contexts

organises and measures time in everyday contexts

measures and uses length in everyday contexts

measures and uses volume, capacity and mass in everyday contexts

measures and uses area in everyday contexts

explores 2-dimensional shapes and 3-dimensional objects

demonstrates knowledge of position and direction in everyday contexts

recognises and represents data in everyday contexts

interprets information from data displays

applies chance and probability to everyday events

estimates, measures and compares the masses of objects using kilograms and grams

represents and interprets analog and digital time in hours, minutes and seconds

applies an understanding of place value and the role of zero to represent numbers to at least tens of thousands

represents and compares decimals up to 2 decimal places using place value

selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers

completes number sentences involving addition and subtraction by finding missing values

applies an understanding of place value and the role of zero to represent numbers to at least tens of thousands

represents and compares decimals up to 2 decimal places using place value

records and compares the results of chance experiments

represents and uses the structure of multiplicative relations to 10 × 10 to solve problems

completes number sentences involving multiplication and division by finding missing values

collects discrete data and constructs graphs using a given scale

interprets data in tables, dot plots and column graphs

uses grid maps and directional language to locate positions and follow routes

measures and estimates lengths in metres, centimetres and millimetres

identifies angles and classifies them by comparing to a right angle

estimates, measures and compares the masses of objects using kilograms and grams

represents and interprets analog and digital time in hours, minutes and seconds

selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers

completes number sentences involving addition and subtraction by finding missing values

makes and sketches models and nets of three-dimensional objects including prisms and pyramids

estimates, measures and compares capacities (internal volumes) using litres, millilitres and volumes using cubic centimetres

compares two-dimensional shapes and describes their features

performs transformations by combining and splitting two-dimensional shapes

estimates, measures and compares areas using square centimetres and square metres

makes and sketches models and nets of three-dimensional objects including prisms and pyramids

estimates, measures and compares capacities (internal volumes) using litres, millilitres and volumes using cubic centimetres

represents and compares halves, quarters, thirds and fifths as lengths on a number line and their related fractions formed by halving (eighths, sixths and tenths)

represents and compares halves, quarters, thirds and fifths as lengths on a number line and their related fractions formed by halving (eighths, sixths and tenths)

records and compares the results of chance experiments

represents and uses the structure of multiplicative relations to 10 × 10 to solve problems

completes number sentences involving multiplication and division by finding missing values

collects discrete data and constructs graphs using a given scale

interprets data in tables, dot plots and column graphs

uses grid maps and directional language to locate positions and follow routes

measures and estimates lengths in metres, centimetres and millimetres

identifies angles and classifies them by comparing to a right angle

compares two-dimensional shapes and describes their features

performs transformations by combining and splitting two-dimensional shapes

estimates, measures and compares areas using square centimetres and square metres

recognises language that represents number

responds to and uses language that represents number

counts in everyday contexts

represents number in everyday contexts

compares and orders numbers

demonstrates knowledge of fractions in everyday contexts

demonstrates knowledge of decimals and percentages in everyday contexts

uses strategies for addition and subtraction

uses strategies for multiplication and division

demonstrates knowledge of money in everyday contexts

plans and manages personal finances

recognises and applies patterns in everyday contexts

demonstrates knowledge of time in everyday contexts

organises and measures time in everyday contexts

measures and uses length in everyday contexts

measures and uses volume, capacity and mass in everyday contexts

measures and uses area in everyday contexts

explores 2-dimensional shapes and 3-dimensional objects

demonstrates knowledge of position and direction in everyday contexts

recognises and represents data in everyday contexts

interprets information from data displays

applies chance and probability to everyday events

applies an understanding of place value and the role of zero to represent the properties of numbers

compares and orders decimals up to 3 decimal places

determines percentages of quantities, and finds equivalent fractions and decimals for benchmark percentage values

constructs graphs using many-to-one scales

interprets data displays, including timelines and line graphs

investigates and classifies two-dimensional shapes, including triangles and quadrilaterals based on their properties

selects and uses the appropriate unit to calculate areas, including areas of rectangles

combines, splits and rearranges shapes to determine the area of parallelograms and triangles

compares and orders fractions with denominators of 2, 3, 4, 5, 6, 8 and 10

selects and applies appropriate strategies to solve multiplication and division problems

constructs and completes number sentences involving multiplicative relations, applying the order of operations to calculations

selects and applies appropriate strategies to solve addition and subtraction problems

locates and describes points on a coordinate plane

selects and uses the appropriate unit and device to measure lengths and distances including perimeters

measures and constructs angles, and identifies the relationships between angles on a straight line and angles at a point

visualises, sketches and constructs three-dimensional objects, including prisms and pyramids, making connections to two-dimensional representations

selects and uses the appropriate unit to estimate, measure and calculate volumes and capacities

conducts chance experiments and quantifies the probability

selects and uses the appropriate unit and device to measure the masses of objects

measures and compares duration, using 12- and 24-hour time and am and pm notation

applies an understanding of place value and the role of zero to represent the properties of numbers

compares and orders decimals up to 3 decimal places

determines percentages of quantities, and finds equivalent fractions and decimals for benchmark percentage values

visualises, sketches and constructs three-dimensional objects, including prisms and pyramids, making connections to two-dimensional representations

selects and uses the appropriate unit to estimate, measure and calculate volumes and capacities

constructs graphs using many-to-one scales

interprets data displays, including timelines and line graphs

compares and orders fractions with denominators of 2, 3, 4, 5, 6, 8 and 10

investigates and classifies two-dimensional shapes, including triangles and quadrilaterals based on their properties

selects and uses the appropriate unit to calculate areas, including areas of rectangles

combines, splits and rearranges shapes to determine the area of parallelograms and triangles

locates and describes points on a coordinate plane

selects and uses the appropriate unit and device to measure lengths and distances including perimeters

measures and constructs angles, and identifies the relationships between angles on a straight line and angles at a point

selects and uses the appropriate unit and device to measure the masses of objects

measures and compares duration, using 12- and 24-hour time and am and pm notation

conducts chance experiments and quantifies the probability

selects and applies appropriate strategies to solve addition and subtraction problems

selects and applies appropriate strategies to solve multiplication and division problems

constructs and completes number sentences involving multiplicative relations, applying the order of operations to calculations

recognises language that represents number

responds to and uses language that represents number

counts in everyday contexts

represents number in everyday contexts

compares and orders numbers

demonstrates knowledge of fractions in everyday contexts

demonstrates knowledge of decimals and percentages in everyday contexts

uses strategies for addition and subtraction

uses strategies for multiplication and division

demonstrates knowledge of money in everyday contexts

plans and manages personal finances

recognises and applies patterns in everyday contexts

demonstrates knowledge of time in everyday contexts

organises and measures time in everyday contexts

measures and uses length in everyday contexts

measures and uses volume, capacity and mass in everyday contexts

measures and uses area in everyday contexts

explores 2-dimensional shapes and 3-dimensional objects

demonstrates knowledge of position and direction in everyday contexts

recognises and represents data in everyday contexts

interprets information from data displays

applies chance and probability to everyday events

compares and orders numbers

classifies and displays data using a variety of graphical representations

explores 2-dimensional shapes and 3-dimensional objects

organises and measures time in everyday contexts

demonstrates knowledge of time in everyday contexts

applies knowledge of area and composite area involving triangles, quadrilaterals and circles to solve problems

measures and uses length in everyday contexts

demonstrates knowledge of fractions in everyday contexts

measures and uses volume, capacity and mass in everyday contexts

applies knowledge of the perimeter of plane shapes and the circumference of circles to solve problems

operates with primes and roots, positive-integer and zero indices involving numerical bases and establishes the relevant index laws

plans and manages personal finances

creates and displays number patterns and finds graphical solutions to problems involving linear relationships

recognises and applies patterns in everyday contexts

identifies and applies the properties of triangles and quadrilaterals to solve problems

compares, orders and calculates with integers to solve problems

applies angle relationships to solve problems, including those related to transversals on sets of parallel lines

applies knowledge of volume and capacity to solve problems involving right prisms and cylinders

applies chance and probability to everyday events

demonstrates knowledge of decimals and percentages in everyday contexts

counts in everyday contexts

measures and uses area in everyday contexts

recognises and represents data in everyday contexts

demonstrates knowledge of position and direction in everyday contexts

applies Pythagoras’ theorem to solve problems in various contexts

represents number in everyday contexts

interprets information from data displays

uses strategies for addition and subtraction

recognises language that represents number

responds to and uses language that represents number

represents and operates with fractions, decimals and percentages to solve problems

demonstrates knowledge of money in everyday contexts

solves problems involving the probabilities of simple chance experiments

analyses simple datasets using measures of centre, range and shape of the data

solves problems involving ratios and rates, and analyses distance–time graphs

uses strategies for multiplication and division

generalises number properties to operate with algebraic expressions including expansion and factorisation

compares and orders numbers

establishes and applies the laws of logarithms to solve problems (Path: Adv)

simplifies algebraic fractions involving indices, and expands and factorises algebraic expressions (Path: Adv)

compares and analyses datasets using summary statistics and graphical representations

solves linear equations of up to 3 steps, limited to one algebraic fraction

simplifies algebraic fractions with numerical denominators and expands algebraic expressions

plans, conducts and reviews a statistical inquiry into a question of interest (Path: Stn, Adv)

explores 2-dimensional shapes and 3-dimensional objects

establishes conditions for congruent triangles and similar triangles and solves problems relating to properties of similar figures and plane shapes (Path: Ext)

applies the index laws to operate with algebraic expressions involving negative-integer indices (Path: Adv)

organises and measures time in everyday contexts

demonstrates knowledge of time in everyday contexts

applies Pythagoras’ theorem and trigonometry to solve 3-dimensional problems and applies the sine, cosine and area rules to solve 2-dimensional problems, including bearings (Path: Stn, Adv)

measures and uses length in everyday contexts

demonstrates knowledge of fractions in everyday contexts

solves problems involving Venn diagrams, 2-way tables and conditional probability (Path: Adv)

measures and uses volume, capacity and mass in everyday contexts

uses function notation to describe and graph functions of one variable and graphs inequalities in one and 2 variables (Path: Adv)

graphs and interprets linear relationships using the gradient/slope-intercept form

solves measurement problems by using scientific notation to represent numbers and rounding to a given number of significant figures

solves linear equations of more than 3 steps, monic and non-monic quadratic equations, and linear simultaneous equations (Path: Adv)

establishes and applies the properties of trigonometric functions and finds solutions to trigonometric equations (Path: Adv)

interprets and compares non-linear relationships and their transformations, both algebraically and graphically (Path: Adv)

plans and manages personal finances

identifies and applies the properties of similar figures and scale drawings to solve problems

applies deductive reasoning to prove circle theorems and solve related problems (Path: Ext)

applies knowledge of the volume of right pyramids, cones and spheres to solve problems involving related composite solids (Path: Stn, Adv)

recognises and applies patterns in everyday contexts

selects and applies appropriate algebraic techniques to operate with algebraic fractions, and expands, factorises and simplifies algebraic expressions (Path: Adv)

determines the midpoint, gradient and length of an interval, and graphs linear relationships, with and without digital tools

describes and performs operations with surds and fractional indices (Path: Adv)

analyses and constructs graphs relating to rates of change (Path: Stn, Adv)

identifies and solves problems involving direct and inverse variation and their graphical representations (Path: Stn, Adv)

identifies and compares features of parabolas and exponential curves in various contexts

applies knowledge of the surface area of right pyramids and cones, spheres and composite solids to solve problems (Path: Stn, Adv)

applies chance and probability to everyday events

demonstrates knowledge of decimals and percentages in everyday contexts

counts in everyday contexts

solves problems involving the volume of composite solids consisting of right prisms and cylinders

measures and uses area in everyday contexts

describes and applies transformations, the midpoint, gradient/slope and distance formulas, and equations of lines to solve problems (Path: Adv)

solves financial problems involving compound interest and depreciation

recognises and represents data in everyday contexts

defines, operates with and graphs polynomials and applies the factor and remainder theorems to solve problems (Path: Adv, Ext)

applies trigonometric ratios to solve right-angled triangle problems

displays and interprets datasets involving bivariate data

demonstrates knowledge of position and direction in everyday contexts

solves financial problems involving simple interest, earning money and spending money

applies trigonometry to solve problems, including bearings and angles of elevation and depression

represents number in everyday contexts

solves problems involving the surface area of right prisms and practical problems involving the area of composite shapes and solids

interprets information from data displays

uses strategies for addition and subtraction

recognises language that represents number

responds to and uses language that represents number

constructs proofs involving congruent triangles and similar triangles and proves properties of plane shapes (Path: Ext)

simplifies algebraic expressions involving positive-integer and zero indices, and establishes the meaning of negative indices for numerical bases

solves problems involving probabilities in multistage chance experiments and simulations

demonstrates knowledge of money in everyday contexts

solves problems involving the characteristics of graphs/networks, planar graphs and Eulerian trails and circuits (Path: Stn)

uses strategies for multiplication and division

identifies connections between algebraic and graphical representations of quadratic and exponential relationships in various contexts

recognises language that represents number

responds to and uses language that represents number

counts in everyday contexts

represents number in everyday contexts

compares and orders numbers

demonstrates knowledge of fractions in everyday contexts

demonstrates knowledge of decimals and percentages in everyday contexts

uses strategies for addition and subtraction

uses strategies for multiplication and division

demonstrates knowledge of money in everyday contexts

plans and manages personal finances

recognises and applies patterns in everyday contexts

demonstrates knowledge of time in everyday contexts

organises and measures time in everyday contexts

measures and uses length in everyday contexts

measures and uses volume, capacity and mass in everyday contexts

measures and uses area in everyday contexts

explores 2-dimensional shapes and 3-dimensional objects

demonstrates knowledge of position and direction in everyday contexts

recognises and represents data in everyday contexts

interprets information from data displays

applies chance and probability to everyday events