The continuum of learning in Mathematics K–10 table is an overview of the substrands, objectives and outcomes in each of the content strands.
The concepts in each of these strands are developed across the stages to show how understanding in the early years needs to precede understanding in later years. In this way, the continuum of learning table provides an overview of the sequence of learning for particular concepts in mathematics and links content that is typically taught in primary mathematics classrooms with content that is typically taught in secondary mathematics classrooms. It illustrates assumptions about prior learning and indicates pathways for further learning.
In this syllabus, it is generally the case that content is not repeated. This is intentional and is not meant to suggest that review and consolidation are not necessary. When programming, it will be necessary for teachers to determine the level of achievement of outcomes in previous stages before planning new teaching and learning experiences. Students may be operating at different stages for different strands of the continuum of learning. For example, a student may be working on Stage 4 content in the Number and Algebra strand but be working on Stage 3 content in the Measurement and Geometry strand.
It is not intended that the continuum of learning table be used as a checklist of teaching ideas. Rather, a variety of learning experiences need to be planned and presented to students to maximise opportunities for achievement of outcomes. Students need appropriate time to explore, experiment and engage with the underpinning concepts and principles of what they are to learn.
Table of objectives and outcomes – Continuum of learning
View the outcomes in an interactive table linked to content.
Download: Continuum of Learning in Mathematics K–10 (A3 PDF, 6 pages, 138KB)
Working Mathematically
Students:
develop understanding and fluency in mathematics through inquiry, exploring and connecting mathematical concepts, choosing and applying problemsolving skills and mathematical techniques, communication and reasoning
EARLY 
STAGE 1 
STAGE 2 
STAGE 3 
STAGE 4 
STAGE 5.1 
STAGE 5.2 
STAGE 5.3 

Communicating MAe1WM describes mathematical situations using everyday language, actions, materials and informal recordings 
Communicating MA11WM describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols 
Communicating MA21WM uses appropriate terminology to describe, and symbols to represent, mathematical ideas 
Communicating MA31WM describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions 
Communicating MA41WM communicates and connects mathematical ideas using appropriate terminology, diagrams and symbols 
Communicating MA5.11WM uses appropriate terminology, diagrams and symbols in mathematical contexts 
Communicating MA5.21WM selects appropriate notations and conventions to communicate mathematical ideas and solutions 
Communicating MA5.31WM uses and interprets formal definitions and generalisations when explaining solutions and/or conjectures 
Problem Solving MAe2WM uses objects, actions, technology and/or trial and error to explore mathematical problems 
Problem Solving MA12WM uses objects, diagrams and technology to explore mathematical problems 
Problem Solving MA22WM selects and uses appropriate mental or written strategies, or technology, to solve problems 
Problem Solving MA32WM selects and applies appropriate problemsolving strategies, including the use of digital technologies, in undertaking investigations 
Problem Solving MA42WM applies appropriate mathematical techniques to solve problems 
Problem Solving MA5.12WM selects and uses appropriate strategies to solve problems 
Problem Solving MA5.22WM interprets mathematical or reallife situations, systematically applying appropriate strategies to solve problems 
Problem Solving MA5.32WM generalises mathematical ideas and techniques to analyse and solve problems efficiently 
Reasoning MAe3WM uses concrete materials and/or pictorial representations to support conclusions 
Reasoning MA13WM supports conclusions by explaining or demonstrating how answers were obtained 
Reasoning MA23WM checks the accuracy of a statement and explains the reasoning used 
Reasoning MA33WM gives a valid reason for supporting one possible solution over another 
Reasoning MA43WM recognises and explains mathematical relationships using reasoning 
Reasoning MA5.13WM provides reasoning to support conclusions that are appropriate to the context 
Reasoning MA5.23WM constructs arguments to prove and justify results 
Reasoning MA5.33WM uses deductive reasoning in presenting arguments and formal proofs 
Number and Algebra
Students:
develop efficient strategies for numerical calculation, recognise patterns, describe relationships and apply algebraic techniques and generalisation
EARLY 
STAGE 1 
STAGE 2 
STAGE 3 
STAGE 4 
STAGE 5.1 
STAGE 5.2 
STAGE 5.3 

Whole Numbers MAe4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20 
Whole Numbers MA14NA applies place value, informally, to count, order, read and represent two and threedigit numbers 
Whole Numbers MA24NA applies place value to order, read and represent numbers of up to five digits 
Whole MA34NA orders, reads and represents integers of any size and describes properties of whole numbers 

Addition and Subtraction MAe5NA combines, separates and compares collections of objects, describes using everyday language, and records using informal methods 
Addition and Subtraction MA15NA uses a range of strategies and informal recording methods for addition and subtraction involving one and twodigit numbers 
Addition and Subtraction MA25NA uses mental and written strategies for addition and subtraction involving two, three, four and fivedigit numbers 
Addition and Subtraction MA35NA selects and applies appropriate strategies for addition and subtraction with counting numbers of any size 
Computation with Integers MA44NA compares, orders and calculates with integers, applying a range of strategies to aid computation 

Multiplication and Division MAe6NA groups, shares and counts collections of objects, describes using everyday language, and records using informal methods 
Multiplication and Division MA16NA uses a range of mental strategies and concrete materials for multiplication and division 
Multiplication and Division MA26NA uses mental and informal written strategies for multiplication and division 
Multiplication and Division MA36NA selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operation 

Fractions and Decimals MAe7NA describes two equal parts as halves 
Fractions and Decimals MA17NA represents and models halves, quarters and eighths 
Fractions and Decimals MA27NA represents, models and compares commonly used fractions and decimals 
Fractions, Decimals and Percentages MA37NA compares, orders and calculates with fractions, decimals and percentages 
Fractions, Decimals and Percentages MA45NA operates with fractions, decimals and percentages 

Financial Mathematics MA46NA solves financial problems involving purchasing goods 
Financial Mathematics MA5.14NA solves financial problems involving earning, spending and investing money 
Financial Mathematics ◊ MA5.24NA solves financial problems involving compound interest 

Ratios and Rates MA47NA operates with ratios and rates, and explores their graphical representation 
Ratios and Rates MA5.25NA recognises direct and indirect proportion, and solves problems involving direct proportion 
Ratios and Rates MA5.34NA draws, interprets and analyses graphs of physical phenomena 

Patterns and Algebra MAe8NA recognises, describes and continues repeating patterns 
Patterns and Algebra MA18NA creates, represents and continues a variety of patterns with numbers and objects 
Patterns and Algebra MA28NA generalises properties of odd and even numbers, generates number patterns, and completes simple number sentences by calculating missing values 
Patterns and Algebra MA38NA analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian plane 
Algebraic Techniques MA48NA generalises number properties to operate with algebraic expressions 
Algebraic Techniques MA5.26NA simplifies algebraic fractions, and expands and factorises quadratic expressions 
Algebraic Techniques § MA5.35NA selects and applies appropriate algebraic techniques to operate with algebraic expressions 

Indices MA49NA operates with positiveinteger and zero indices of numerical bases 
Indices MA5.15NA operates with algebraic expressions involving positiveinteger and zero indices, and establishes the meaning of negative indices for numerical bases 
Indices MA5.27NA applies index laws to operate with algebraic expressions involving integer indices 
Surds and Indices § MA5.36NA performs operations with surds and indices 

Equations MA410NA uses algebraic techniques to solve simple linear and quadratic equations 
Equations MA5.28NA solves linear and simple quadratic equations, linear inequalities and linear simultaneous equations, using analytical and graphical techniques 
Equations § MA5.37NA solves complex linear, quadratic, simple cubic and simultaneous equations, and rearranges literal equations 

Linear Relationships MA411NA creates and displays number patterns; graphs and analyses linear relationships; and performs transformations on the Cartesian plane 
Linear Relationships MA5.16NA determines the midpoint, gradient and length of an interval, and graphs linear relationships 
Linear Relationships ◊ MA5.29NA uses the gradientintercept form to interpret and graph linear relationships 
Linear Relationships § MA5.38NA uses formulas to find midpoint, gradient and distance on the Cartesian plane, and applies standard forms of the equation of a straight line 

NonLinear Relationships MA5.17NA graphs simple nonlinear relationships 
NonLinear Relationships ◊ MA5.210NA connects algebraic and graphical representations of simple nonlinear relationships 
NonLinear Relationships § MA5.39NA sketches and interprets a variety of nonlinear relationships 

Polynomials # MA5.310NA recognises, describes and sketches polynomials, and applies the factor and remainder theorems to solve problems 

Logarithms # MA5.311NA uses the definition of a logarithm to establish and apply the laws of logarithms 

Functions and Other Graphs # MA5.312NA uses function notation to describe and sketch functions 
Measurement and Geometry
Students:
identify, visualise and quantify measures and the attributes of shapes and objects, and explore measurement concepts and geometric relationships, applying formulas, strategies and geometric reasoning in the solution of problems
EARLY 
STAGE 1 
STAGE 2 
STAGE 3 
STAGE 4 
STAGE 5.1 
STAGE 5.2 
STAGE 5.3 

Length MAe9MG describes and compares lengths and distances using everyday language 
Length MA19MG measures, records, compares and estimates lengths and distances using uniform informal units, metres and centimetres 
Length MA29MG measures, records, compares and estimates lengths, distances and perimeters in metres, centimetres and millimetres, and measures, compares and records temperatures 
Length MA39MG selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length 
Length MA412MG calculates the perimeters of plane shapes and the circumferences of circles 

Area MAe10MG describes and compares areas using everyday language 
Area MA110MG measures, records, compares and estimates areas using uniform informal units 
Area MA210MG measures, records, compares and estimates areas using square centimetres and square metres 
Area MA310MG selects and uses the appropriate unit to calculate areas, including areas of squares, rectangles and triangles 
Area MA413MG uses formulas to calculate the areas of quadrilaterals and circles, and converts between units of area 
Area and Surface Area MA5.18MG calculates the areas of composite shapes, and the surface areas of rectangular and triangular prisms 
Area and Surface Area MA5.211MG calculates the surface areas of right prisms, cylinders and related composite solids 
Area and Surface Area MA5.313MG applies formulas to find the surface areas of right pyramids, right cones, spheres and related composite solids 
Volume and Capacity MAe11MG describes and compares the capacities of containers and the volumes of objects or substances using everyday language 
Volume and Capacity MA111MG measures, records, compares and estimates volumes and capacities using uniform informal units 
Volume and Capacity MA211MG measures, records, compares and estimates volumes and capacities using litres, millilitres and cubic centimetres 
Volume and Capacity MA311MG selects and uses the appropriate unit to estimate, measure and calculate volumes and capacities, and converts between units of capacity 
Volume MA414MG uses formulas to calculate the volumes of prisms and cylinders, and converts between units of volume 
Volume MA5.212MG applies formulas to calculate the volumes of composite solids composed of right prisms and cylinders 
Volume MA5.314MG applies formulas to find the volumes of right pyramids, right cones, spheres and related composite solids 

Mass MAe12MG describes and compares the masses of objects using everyday language 
Mass MA112MG measures, records, compares and estimates the masses of objects using uniform informal units 
Mass MA212MG measures, records, compares and estimates the masses of objects using kilograms and grams 
Mass MA312MG selects and uses the appropriate unit and device to measure the masses of objects, and converts between units of mass 

Time MAe13MG sequences events, uses everyday language to describe the durations of events, and reads hour time on clocks 
Time MA113MG describes, compares and orders durations of events, and reads half and quarterhour time 
Time MA213MG reads and records time in oneminute intervals and converts between hours, minutes and seconds 
Time MA313MG uses 24hour time and am and pm notation in reallife situations, and constructs timelines 
Time MA415MG performs calculations of time that involve mixed units, and interprets time zones 
Numbers of Any Magnitude MA5.19MG interprets very small and very large units of measurement, uses scientific notation, and rounds to significant figures 

RightAngled Triangles (Pythagoras) MA416MG applies Pythagoras’ theorem to calculate side lengths in rightangled triangles, and solves related problems 
RightAngled Triangles (Trigonometry) MA5.110MG applies trigonometry, given diagrams, to solve problems, including problems involving angles of elevation and depression 
RightAngled Triangles (Trigonometry) ◊ MA5.213MG applies trigonometry to solve problems, including problems involving bearings 
Trigonometry and Pythagoras' Theorem § MA5.315MG applies Pythagoras’ theorem, trigonometric relationships, the sine rule, the cosine rule and the area rule to solve problems, including problems involving three dimensions 

ThreeDimensional MAe14MG manipulates, sorts and represents threedimensional objects and describes them using everyday language 
ThreeDimensional MA114MG sorts, describes, represents and recognises familiar threedimensional objects, including cones, cubes, cylinders, spheres and prisms 
ThreeDimensional MA214MG makes, compares, sketches and names threedimensional objects, including prisms, pyramids, cylinders, cones and spheres, and describes their features 
ThreeDimensional MA314MG identifies threedimensional objects, including prisms and pyramids, on the basis of their properties, and visualises, sketches and constructs them given drawings of different views 

TwoDimensional Space MAe15MG manipulates, sorts and describes representations of twodimensional shapes, including circles, triangles, squares and rectangles, using everyday language 
TwoDimensional MA115MG manipulates, sorts, represents, describes and explores twodimensional shapes, including quadrilaterals, pentagons, hexagons and octagons 
TwoDimensional MA215MG manipulates, identifies and sketches twodimensional shapes, including special quadrilaterals, and describes their features 
TwoDimensional MA315MG manipulates, classifies and draws twodimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties 
Properties of Geometrical Figures MA417MG classifies, describes and uses the properties of triangles and quadrilaterals, and determines congruent triangles to find unknown side lengths and angles 
Properties of Geometrical Figures MA5.111MG describes and applies the properties of similar figures and scale drawings 
Properties of Geometrical Figures MA5.214MG calculates the angle sum of any polygon and uses minimum conditions to prove triangles are congruent or similar 
Properties of Geometrical Figures § MA5.316MG proves triangles are similar, and uses formal geometric reasoning to establish properties of triangles and quadrilaterals 
Angles MA216MG identifies, describes, compares and classifies angles 
Angles MA316MG measures and constructs angles, and applies angle relationships to find unknown angles 
Angle Relationships MA418MG identifies and uses angle relationships, including those related to transversals on sets of parallel lines 

Position MAe16MG describes position and gives and follows simple directions using everyday language 
Position MA116MG represents and describes the positions of objects in everyday situations and on maps 
Position MA217MG uses simple maps and grids to represent position and follow routes, including using compass directions 
Position MA317MG locates and describes position on maps using a gridreference system 

Circle Geometry # MA5.317MG applies deductive reasoning to prove circle theorems and to solve related problems 
Statistics and Probability
Students:
collect, represent, analyse, interpret and evaluate data, assign and use probabilities, and make sound judgements
EARLY 
STAGE 1 
STAGE 2 
STAGE 3 
STAGE 4 
STAGE 5.1 
STAGE 5.2 
STAGE 5.3 

Data MAe17SP represents data and interprets data displays made from objects 
Data MA117SP gathers and organises data, displays data in lists, tables and picture graphs, and interprets the results 
Data MA218SP selects appropriate methods to collect data, and constructs, compares, interprets and evaluates data displays, including tables, picture graphs and column graphs 
Data MA318SP uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots, line graphs and twoway tables 
Data Collection and Representation MA419SP collects, represents and interprets single sets of data, using appropriate statistical displays 

Single Variable Data Analysis MA420SP analyses single sets of data using measures of location, and range 
Single Variable Data Analysis MA5.112SP uses statistical displays to compare sets of data, and evaluates statistical claims made in the media 
Single Variable Data Analysis ◊ MA5.215SP uses quartiles and box plots to compare sets of data, and evaluates sources of data 
Single Variable Data Analysis § MA5.318SP uses standard deviation to analyse data 

Bivariate Data Analysis MA5.216SP investigates relationships between two statistical variables, including their relationship over time 
Bivariate Data Analysis MA5.319SP investigates the relationship between numerical variables using lines of best fit, and explores how data is used to inform decisionmaking processes 

Chance MA118SP recognises and describes the element of chance in everyday events 
Chance MA219SP describes and compares chance events in social and experimental contexts 
Chance MA319SP conducts chance experiments and assigns probabilities as values between 0 and 1 to describe their outcomes 
Probability MA421SP represents probabilities of simple and compound events 
Probability MA5.113SP calculates relative frequencies to estimate probabilities of simple and compound events 
Probability ◊ MA5.217SP describes and calculates probabilities in multistep chance experiments 
For an explanation of the use of the symbols ◊, § and #, see Mathematics learning in Stage 5.
Years 7–10 Life Skills Outcomes
For some students with special education needs, particularly those students with an intellectual disability, it may be determined that the Stage 4 and Stage 5 outcomes and content are not appropriate. For these students, Life Skills outcomes and content can provide a relevant and meaningful program. Refer to the Introduction for further information about curriculum options for students with special education needs. Years 7–10 Life Skills outcomes and content are in the Life Skills section of the syllabus.