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NSW Syllabuses

Outcomes

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 problem-solving skills and mathematical techniques, communication and reasoning

EARLY
STAGE 1

STAGE 1

STAGE 2

STAGE 3

STAGE 4

STAGE 5.1

STAGE 5.2

STAGE 5.3

Communicating

MAe-1WM describes mathematical situations using everyday language, actions, materials and informal recordings

Communicating

MA1-1WM describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols

Communicating

MA2-1WM uses appropriate terminology to describe, and symbols to represent, mathematical ideas

Communicating

MA3-1WM describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions

Communicating

MA4-1WM communicates and connects mathematical ideas using appropriate terminology, diagrams and symbols

Communicating

MA5.1-1WM uses appropriate terminology, diagrams and symbols in mathematical contexts

Communicating

MA5.2-1WM selects appropriate notations and conventions to communicate mathematical ideas and solutions

Communicating

MA5.3-1WM uses and interprets formal definitions and generalisations when explaining solutions and/or conjectures

Problem Solving

MAe-2WM uses objects, actions, technology and/or trial and error to explore mathematical problems

Problem Solving

MA1-2WM uses objects, diagrams and technology to explore mathematical problems

Problem Solving

MA2-2WM selects and uses appropriate mental or written strategies, or technology, to solve problems

Problem Solving

MA3-2WM selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations

Problem Solving

MA4-2WM applies appropriate mathematical techniques to solve problems

Problem Solving

MA5.1-2WM selects and uses appropriate strategies to solve problems

Problem Solving

MA5.2-2WM interprets mathematical or real-life situations, systematically applying appropriate strategies to solve problems

Problem Solving

MA5.3-2WM generalises mathematical ideas and techniques to analyse and solve problems efficiently

Reasoning

MAe-3WM uses concrete materials and/or pictorial representations to support conclusions

Reasoning

MA1-3WM supports conclusions by explaining or demonstrating how answers were obtained

Reasoning

MA2-3WM checks the accuracy of a statement and explains the reasoning used

Reasoning

MA3-3WM gives a valid reason for supporting one possible solution over another

Reasoning

MA4-3WM recognises and explains mathematical relationships using reasoning

Reasoning

MA5.1-3WM provides reasoning to support conclusions that are appropriate to the context

Reasoning

MA5.2-3WM constructs arguments to prove and justify results

Reasoning

MA5.3-3WM 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 1

STAGE 2

STAGE 3

STAGE 4

STAGE 5.1

STAGE 5.2

STAGE 5.3

Whole Numbers

MAe-4NA counts to 30, and orders, reads and represents numbers in the range 0 to 20

Whole Numbers

MA1-4NA applies place value, informally, to count, order, read and represent two- and three-digit numbers

Whole Numbers

MA2-4NA applies place value to order, read and represent numbers of up to five digits

Whole
Numbers

MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers

       

Addition and Subtraction

MAe-5NA combines, separates and compares collections of objects, describes using everyday language, and records using informal methods

Addition and Subtraction

MA1-5NA uses a range of strategies and informal recording methods for addition and subtraction involving one- and two-digit numbers

Addition and Subtraction

MA2-5NA uses mental and written strategies for addition and subtraction involving two-, three-, four- and five-digit numbers

Addition and Subtraction

MA3-5NA selects and applies appropriate strategies for addition and subtraction with counting numbers of any size

Computation with Integers

MA4-4NA compares, orders and calculates with integers, applying a range of strategies to aid computation

     

Multiplication and Division

MAe-6NA groups, shares and counts collections of objects, describes using everyday language, and records using informal methods

Multiplication and Division

MA1-6NA uses a range of mental strategies and concrete materials for multiplication and division

Multiplication and Division

MA2-6NA uses mental and informal written strategies for multiplication and division

Multiplication and Division

MA3-6NA 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

MAe-7NA describes two equal parts as halves

Fractions and Decimals

MA1-7NA represents and models halves, quarters and eighths

Fractions and Decimals

MA2-7NA represents, models and compares commonly used fractions and decimals

Fractions, Decimals and Percentages

MA3-7NA compares, orders and calculates with fractions, decimals and percentages

Fractions, Decimals and Percentages

MA4-5NA operates with fractions, decimals and percentages

     
       

Financial Mathematics

MA4-6NA solves financial problems involving purchasing goods

Financial Mathematics

MA5.1-4NA solves financial problems involving earning, spending and investing money

Financial Mathematics ◊

MA5.2-4NA solves financial problems involving compound interest

 
       

Ratios and Rates

MA4-7NA operates with ratios and rates, and explores their graphical representation

 

Ratios and Rates

MA5.2-5NA recognises direct and indirect proportion, and solves problems involving direct proportion

Ratios and Rates

MA5.3-4NA draws, interprets and analyses graphs of physical phenomena

Patterns and Algebra

MAe-8NA recognises, describes and continues repeating patterns

Patterns and Algebra

MA1-8NA creates, represents and continues a variety of patterns with numbers and objects

Patterns and Algebra

MA2-8NA generalises properties of odd and even numbers, generates number patterns, and completes simple number sentences by calculating missing values

Patterns and Algebra

MA3-8NA analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian plane

Algebraic Techniques

MA4-8NA generalises number properties to operate with algebraic expressions

 

Algebraic Techniques

MA5.2-6NA simplifies algebraic fractions, and expands and factorises quadratic expressions

Algebraic Techniques §

MA5.3-5NA selects and applies appropriate algebraic techniques to operate with algebraic expressions

       

Indices

MA4-9NA operates with positive-integer and zero indices of numerical bases

Indices

MA5.1-5NA operates with algebraic expressions involving positive-integer and zero indices, and establishes the meaning of negative indices for numerical bases

Indices

MA5.2-7NA applies index laws to operate with algebraic expressions involving integer indices

Surds and Indices §

MA5.3-6NA performs operations with surds and indices

       

Equations

MA4-10NA uses algebraic techniques to solve simple linear and quadratic equations

 

Equations

MA5.2-8NA solves linear and simple quadratic equations, linear inequalities and linear simultaneous equations, using analytical and graphical techniques

Equations §

MA5.3-7NA solves complex linear, quadratic, simple cubic and simultaneous equations, and rearranges literal equations

       

Linear Relationships

MA4-11NA creates and displays number patterns; graphs and analyses linear relationships; and performs transformations on the Cartesian plane

Linear Relationships

MA5.1-6NA determines the midpoint, gradient and length of an interval, and graphs linear relationships

Linear Relationships

MA5.2-9NA uses the gradient-intercept form to interpret and graph linear relationships

Linear Relationships §

MA5.3-8NA uses formulas to find midpoint, gradient and distance on the Cartesian plane, and applies standard forms of the equation of a straight line

         

Non-Linear Relationships

MA5.1-7NA graphs simple non-linear relationships

Non-Linear Relationships ◊

MA5.2-10NA connects algebraic and graphical representations of simple non-linear relationships

Non-Linear Relationships §

MA5.3-9NA sketches and interprets a variety of non-linear relationships

             

Polynomials #

MA5.3-10NA recognises, describes and sketches polynomials, and applies the factor and remainder theorems to solve problems

             

Logarithms #

MA5.3-11NA uses the definition of a logarithm to establish and apply the laws of logarithms

             

Functions and Other Graphs #

MA5.3-12NA 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 1

STAGE 2

STAGE 3

STAGE 4

STAGE 5.1

STAGE 5.2

STAGE 5.3

Length

MAe-9MG describes and compares lengths and distances using everyday language

Length

MA1-9MG measures, records, compares and estimates lengths and distances using uniform informal units, metres and centimetres

Length

MA2-9MG measures, records, compares and estimates lengths, distances and perimeters in metres, centimetres and millimetres, and measures, compares and records temperatures

Length

MA3-9MG selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length

Length

MA4-12MG calculates the perimeters of plane shapes and the circumferences of circles

     

Area

MAe-10MG describes and compares areas using everyday language

Area

MA1-10MG measures, records, compares and estimates areas using uniform informal units

Area

MA2-10MG measures, records, compares and estimates areas using square centimetres and square metres

Area

MA3-10MG selects and uses the appropriate unit to calculate areas, including areas of squares, rectangles and triangles

Area

MA4-13MG uses formulas to calculate the areas of quadrilaterals and circles, and converts between units of area

Area and Surface Area

MA5.1-8MG calculates the areas of composite shapes, and the surface areas of rectangular and triangular prisms

Area and Surface Area

MA5.2-11MG calculates the surface areas of right prisms, cylinders and related composite solids

Area and Surface Area

MA5.3-13MG applies formulas to find the surface areas of right pyramids, right cones, spheres and related composite solids

Volume and Capacity

MAe-11MG describes and compares the capacities of containers and the volumes of objects or substances using everyday language

Volume and Capacity

MA1-11MG measures, records, compares and estimates volumes and capacities using uniform informal units

Volume and Capacity

MA2-11MG measures, records, compares and estimates volumes and capacities using litres, millilitres and cubic centimetres

Volume and Capacity

MA3-11MG selects and uses the appropriate unit to estimate, measure and calculate volumes and capacities, and converts between units of capacity

Volume

MA4-14MG uses formulas to calculate the volumes of prisms and cylinders, and converts between units of volume

 

Volume

MA5.2-12MG applies formulas to calculate the volumes of composite solids composed of right prisms and cylinders

Volume

MA5.3-14MG applies formulas to find the volumes of right pyramids, right cones, spheres and related composite solids

Mass

MAe-12MG describes and compares the masses of objects using everyday language

Mass

MA1-12MG measures, records, compares and estimates the masses of objects using uniform informal units

Mass

MA2-12MG measures, records, compares and estimates the masses of objects using kilograms and grams

Mass

MA3-12MG selects and uses the appropriate unit and device to measure the masses of objects, and converts between units of mass

       

Time

MAe-13MG sequences events, uses everyday language to describe the durations of events, and reads hour time on clocks

Time

MA1-13MG describes, compares and orders durations of events, and reads half- and quarter-hour time

Time

MA2-13MG reads and records time in one-minute intervals and converts between hours, minutes and seconds

Time

MA3-13MG uses 24-hour time and am and pm notation in real-life situations, and constructs timelines

Time

MA4-15MG performs calculations of time that involve mixed units, and interprets time zones

Numbers of Any Magnitude

MA5.1-9MG interprets very small and very large units of measurement, uses scientific notation, and rounds to significant figures

   
       

Right-Angled Triangles (Pythagoras)

MA4-16MG applies Pythagoras’ theorem to calculate side lengths in right-angled triangles, and solves related problems

Right-Angled Triangles (Trigonometry)

MA5.1-10MG applies trigonometry, given diagrams, to solve problems, including problems involving angles of elevation and depression

Right-Angled Triangles (Trigonometry) ◊

MA5.2-13MG applies trigonometry to solve problems, including problems involving bearings

Trigonometry and Pythagoras' Theorem §

MA5.3-15MG applies Pythagoras’ theorem, trigonometric relationships, the sine rule, the cosine rule and the area rule to solve problems, including problems involving three dimensions

Three-Dimensional
Space

MAe-14MG manipulates, sorts and represents three-dimensional objects and describes them using everyday language

Three-Dimensional
Space

MA1-14MG sorts, describes, represents and recognises familiar three-dimensional objects, including cones, cubes, cylinders, spheres and prisms

Three-Dimensional
Space

MA2-14MG makes, compares, sketches and names three-dimensional objects, including prisms, pyramids, cylinders, cones and spheres, and describes their features

Three-Dimensional
Space

MA3-14MG identifies three-dimensional objects, including prisms and pyramids, on the basis of their properties, and visualises, sketches and constructs them given drawings of different views

     

Two-Dimensional Space

MAe-15MG manipulates, sorts and describes representations of two-dimensional shapes, including circles, triangles, squares and rectangles, using everyday language

Two-Dimensional
Space

MA1-15MG manipulates, sorts, represents, describes and explores two-dimensional shapes, including quadrilaterals, pentagons, hexagons and octagons

Two-Dimensional
Space

MA2-15MG manipulates, identifies and sketches two-dimensional shapes, including special quadrilaterals, and describes their features

Two-Dimensional
Space

MA3-15MG manipulates, classifies and draws two-dimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties

Properties of Geometrical Figures

MA4-17MG 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

MA5.1-11MG describes and applies the properties of similar figures and scale drawings

Properties of Geometrical Figures

MA5.2-14MG calculates the angle sum of any polygon and uses minimum conditions to prove triangles are congruent or similar

Properties of Geometrical Figures §

MA5.3-16MG proves triangles are similar, and uses formal geometric reasoning to establish properties of triangles and quadrilaterals

   

Angles

MA2-16MG identifies, describes, compares and classifies angles

Angles

MA3-16MG measures and constructs angles, and applies angle relationships to find unknown angles

Angle Relationships

MA4-18MG identifies and uses angle relationships, including those related to transversals on sets of parallel lines

     

Position

MAe-16MG describes position and gives and follows simple directions using everyday language

Position

MA1-16MG represents and describes the positions of objects in everyday situations and on maps

Position

MA2-17MG uses simple maps and grids to represent position and follow routes, including using compass directions

Position

MA3-17MG locates and describes position on maps using a grid-reference system

       
             

Circle Geometry #

MA5.3-17MG 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 1

STAGE 2

STAGE 3

STAGE 4

STAGE 5.1

STAGE 5.2

STAGE 5.3

Data

MAe-17SP represents data and interprets data displays made from objects

Data

MA1-17SP gathers and organises data, displays data in lists, tables and picture graphs, and interprets the results

Data

MA2-18SP selects appropriate methods to collect data, and constructs, compares, interprets and evaluates data displays, including tables, picture graphs and column graphs

Data

MA3-18SP uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots, line graphs and two-way tables

Data Collection and Representation

MA4-19SP collects, represents and interprets single sets of data, using appropriate statistical displays

     

Single Variable Data Analysis

MA4-20SP analyses single sets of data using measures of location, and range

Single Variable Data Analysis

MA5.1-12SP uses statistical displays to compare sets of data, and evaluates statistical claims made in the media

Single Variable Data Analysis ◊

MA5.2-15SP uses quartiles and box plots to compare sets of data, and evaluates sources of data

Single Variable Data Analysis

MA5.3-18SP uses standard deviation to analyse data

           

Bivariate Data Analysis

MA5.2-16SP investigates relationships between two statistical variables, including their relationship over time

Bivariate Data Analysis

MA5.3-19SP investigates the relationship between numerical variables using lines of best fit, and explores how data is used to inform decision-making processes

 

Chance

MA1-18SP recognises and describes the element of chance in everyday events

Chance

MA2-19SP describes and compares chance events in social and experimental contexts

Chance

MA3-19SP conducts chance experiments and assigns probabilities as values between 0 and 1 to describe their outcomes

Probability

MA4-21SP represents probabilities of simple and compound events

Probability

MA5.1-13SP calculates relative frequencies to estimate probabilities of simple and compound events

Probability

MA5.2-17SP describes and calculates probabilities in multi-step 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.