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NSW Syllabuses

Outcomes

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
outcomes

A student:

Stage 1
outcomes

A student:

Stage 2
outcomes

A student:

Stage 3
outcomes

A student:

Stage 4
outcomes

A student:

Stage 5.1
outcomes

A student:

Stage 5.2
outcomes

A student:

Stage 5.3
outcomes

A student:
  • describes mathematical situations using everyday language, actions, materials and informal recordings

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

    MA1-1WM
  • uses appropriate terminology to describe, and symbols to represent, mathematical ideas

    MA2-1WM
  • describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions

    MA3-1WM
  • communicates and connects mathematical ideas using appropriate terminology, diagrams and symbols

    MA4-1WM
  • uses appropriate terminology, diagrams and symbols in mathematical contexts

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

    MA5.2-1WM
  • uses and interprets formal definitions and generalisations when explaining solutions and/or conjectures

    MA5.3-1WM
  • uses objects, actions, technology and/or trial and error to explore mathematical problems

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

    MA1-2WM
  • selects and uses appropriate mental or written strategies, or technology, to solve problems

    MA2-2WM
  • selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations

    MA3-2WM
  • applies appropriate mathematical techniques to solve problems

    MA4-2WM
  • selects and uses appropriate strategies to solve problems

    MA5.1-2WM
  • interprets mathematical or real-life situations, systematically applying appropriate strategies to solve problems

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

    MA5.3-2WM
  • uses concrete materials and/or pictorial representations to support conclusions

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

    MA1-3WM
  • checks the accuracy of a statement and explains the reasoning used

    MA2-3WM
  • gives a valid reason for supporting one possible solution over another

    MA3-3WM
  • recognises and explains mathematical relationships using reasoning

    MA4-3WM
  • provides reasoning to support conclusions that are appropriate to the context

    MA5.1-3WM
  • constructs arguments to prove and justify results

    MA5.2-3WM
  • uses deductive reasoning in presenting arguments and formal proofs

    MA5.3-3WM

 

Number and Algebra

Students:
  • develop efficient strategies for numerical calculation, recognise patterns, describe relationships and apply algebraic techniques and generalisation

Early Stage 1
outcomes

A student:

Stage 1
outcomes

A student:

Stage 2
outcomes

A student:

Stage 3
outcomes

A student:

Stage 4
outcomes

A student:

Stage 5.1
outcomes

A student:

Stage 5.2
outcomes

A student:

Stage 5.3
outcomes

A student:
  • counts to 30, and orders, reads and represents numbers in the range 0 to 20

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

    MA1-4NA
  • applies place value to order, read and represent numbers of up to five digits

    MA2-4NA
  • orders, reads and represents integers of any size and describes properties of whole numbers

    MA3-4NA
  • combines, separates and compares collections of objects, describes using everyday language, and records using informal methods

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

    MA1-5NA
  • uses mental and written strategies for addition and subtraction involving two-, three-, four- and five-digit numbers

    MA2-5NA
  • selects and applies appropriate strategies for addition and subtraction with counting numbers of any size

    MA3-5NA
  • compares, orders and calculates with integers, applying a range of strategies to aid computation

    MA4-4NA
  • groups, shares and counts collections of objects, describes using everyday language, and records using informal methods

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

    MA1-6NA
  • uses mental and informal written strategies for multiplication and division

    MA2-6NA
  • selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operation

    MA3-6NA
  • describes two equal parts as halves

    MAe-7NA
  • represents and models halves, quarters and eighths

    MA1-7NA
  • represents, models and compares commonly used fractions and decimals

    MA2-7NA
  • compares, orders and calculates with fractions, decimals and percentages

    MA3-7NA
  • operates with fractions, decimals and percentages

    MA4-5NA
  • solves financial problems involving purchasing goods

    MA4-6NA
  • solves financial problems involving earning, spending and investing money

    MA5.1-4NA
  • solves financial problems involving compound interest

    MA5.2-4NA
  • operates with ratios and rates, and explores their graphical representation

    MA4-7NA
  • recognises direct and indirect proportion, and solves problems involving direct proportion

    MA5.2-5NA
  • draws, interprets and analyses graphs of physical phenomena

    MA5.3-4NA
  • recognises, describes and continues repeating patterns

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

    MA1-8NA
  • generalises properties of odd and even numbers, generates number patterns, and completes simple number sentences by calculating missing values

    MA2-8NA
  • analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian plane

    MA3-8NA
  • generalises number properties to operate with algebraic expressions

    MA4-8NA
  • simplifies algebraic fractions, and expands and factorises quadratic expressions

    MA5.2-6NA
  • selects and applies appropriate algebraic techniques to operate with algebraic expressions

    MA5.3-5NA
  • operates with positive-integer and zero indices of numerical bases

    MA4-9NA
  • operates with algebraic expressions involving positive-integer and zero indices, and establishes the meaning of negative indices for numerical bases

    MA5.1-5NA
  • applies index laws to operate with algebraic expressions involving integer indices

    MA5.2-7NA
  • performs operations with surds and indices

    MA5.3-6NA
  • uses algebraic techniques to solve simple linear and quadratic equations

    MA4-10NA
  • solves linear and simple quadratic equations, linear inequalities and linear simultaneous equations, using analytical and graphical techniques

    MA5.2-8NA
  • solves complex linear, quadratic, simple cubic and simultaneous equations, and rearranges literal equations

    MA5.3-7NA
  • creates and displays number patterns; graphs and analyses linear relationships; and performs transformations on the Cartesian plane

    MA4-11NA
  • determines the midpoint, gradient and length of an interval, and graphs linear relationships

    MA5.1-6NA
  • uses the gradient-intercept form to interpret and graph linear relationships

    MA5.2-9NA
  • uses formulas to find midpoint, gradient and distance on the Cartesian plane, and applies standard forms of the equation of a straight line

    MA5.3-8NA
  • graphs simple non-linear relationships

    MA5.1-7NA
  • connects algebraic and graphical representations of simple non-linear relationships

    MA5.2-10NA
  • sketches and interprets a variety of non-linear relationships

    MA5.3-9NA
  • recognises, describes and sketches polynomials, and applies the factor and remainder theorems to solve problems

    MA5.3-10NA
  • uses the definition of a logarithm to establish and apply the laws of logarithms

    MA5.3-11NA
  • uses function notation to describe and sketch functions

    MA5.3-12NA

 

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
outcomes

A student:

Stage 1
outcomes

A student:

Stage 2
outcomes

A student:

Stage 3
outcomes

A student:

Stage 4
outcomes

A student:

Stage 5.1
outcomes

A student:

Stage 5.2
outcomes

A student:

Stage 5.3
outcomes

A student:
  • describes and compares lengths and distances using everyday language

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

    MA1-9MG
  • measures, records, compares and estimates lengths, distances and perimeters in metres, centimetres and millimetres, and measures, compares and records temperatures

    MA2-9MG
  • selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length

    MA3-9MG
  • calculates the perimeters of plane shapes and the circumferences of circles

    MA4-12MG
  • describes and compares areas using everyday language

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

    MA1-10MG
  • measures, records, compares and estimates areas using square centimetres and square metres

    MA2-10MG
  • selects and uses the appropriate unit to calculate areas, including areas of squares, rectangles and triangles

    MA3-10MG
  • uses formulas to calculate the areas of quadrilaterals and circles, and converts between units of area

    MA4-13MG
  • calculates the areas of composite shapes, and the surface areas of rectangular and triangular prisms

    MA5.1-8MG
  • calculates the surface areas of right prisms, cylinders and related composite solids

    MA5.2-11MG
  • applies formulas to find the surface areas of right pyramids, right cones, spheres and related composite solids

    MA5.3-13MG
  • describes and compares the capacities of containers and the volumes of objects or substances using everyday language

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

    MA1-11MG
  • measures, records, compares and estimates volumes and capacities using litres, millilitres and cubic centimetres

    MA2-11MG
  • selects and uses the appropriate unit to estimate, measure and calculate volumes and capacities, and converts between units of capacity

    MA3-11MG
  • uses formulas to calculate the volumes of prisms and cylinders, and converts between units of volume

    MA4-14MG
  • applies formulas to calculate the volumes of composite solids composed of right prisms and cylinders

    MA5.2-12MG
  • applies formulas to find the volumes of right pyramids, right cones, spheres and related composite solids

    MA5.3-14MG
  • describes and compares the masses of objects using everyday language

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

    MA1-12MG
  • measures, records, compares and estimates the masses of objects using kilograms and grams

    MA2-12MG
  • selects and uses the appropriate unit and device to measure the masses of objects, and converts between units of mass

    MA3-12MG
  • sequences events, uses everyday language to describe the durations of events, and reads hour time on clocks

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

    MA1-13MG
  • reads and records time in one-minute intervals and converts between hours, minutes and seconds

    MA2-13MG
  • uses 24-hour time and am and pm notation in real-life situations, and constructs timelines

    MA3-13MG
  • performs calculations of time that involve mixed units, and interprets time zones

    MA4-15MG
  • interprets very small and very large units of measurement, uses scientific notation, and rounds to significant figures

    MA5.1-9MG
  • applies Pythagoras’ theorem to calculate side lengths in right-angled triangles, and solves related problems

    MA4-16MG
  • applies trigonometry, given diagrams, to solve problems, including problems involving angles of elevation and depression

    MA5.1-10MG
  • applies trigonometry to solve problems, including problems involving bearings

    MA5.2-13MG
  • applies Pythagoras’ theorem, trigonometric relationships, the sine rule, the cosine rule and the area rule to solve problems, including problems involving three dimensions

    MA5.3-15MG
  • manipulates, sorts and represents three-dimensional objects and describes them using everyday language

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

    MA1-14MG
  • makes, compares, sketches and names three-dimensional objects, including prisms, pyramids, cylinders, cones and spheres, and describes their features

    MA2-14MG
  • 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

    MA3-14MG
  • manipulates, sorts and describes representations of two-dimensional shapes, including circles, triangles, squares and rectangles, using everyday language

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

    MA1-15MG
  • manipulates, identifies and sketches two-dimensional shapes, including special quadrilaterals, and describes their features

    MA2-15MG
  • manipulates, classifies and draws two-dimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties

    MA3-15MG
  • classifies, describes and uses the properties of triangles and quadrilaterals, and determines congruent triangles to find unknown side lengths and angles

    MA4-17MG
  • describes and applies the properties of similar figures and scale drawings

    MA5.1-11MG
  • calculates the angle sum of any polygon and uses minimum conditions to prove triangles are congruent or similar

    MA5.2-14MG
  • proves triangles are similar, and uses formal geometric reasoning to establish properties of triangles and quadrilaterals

    MA5.3-16MG
  • identifies, describes, compares and classifies angles

    MA2-16MG
  • measures and constructs angles, and applies angle relationships to find unknown angles

    MA3-16MG
  • identifies and uses angle relationships, including those related to transversals on sets of parallel lines

    MA4-18MG
  • applies deductive reasoning to prove circle theorems and to solve related problems

    MA5.3-17MG
  • describes position and gives and follows simple directions using everyday language

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

    MA1-16MG
  • uses simple maps and grids to represent position and follow routes, including using compass directions

    MA2-17MG
  • locates and describes position on maps using a grid-reference system

    MA3-17MG

 

Statistics and Probability

Students:
  • collect, represent, analyse, interpret and evaluate data, assign and use probabilities, and make sound judgements

Early Stage 1
outcomes

A student:

Stage 1
outcomes

A student:

Stage 2
outcomes

A student:

Stage 3
outcomes

A student:

Stage 4
outcomes

A student:

Stage 5.1
outcomes

A student:

Stage 5.2
outcomes

A student:

Stage 5.3
outcomes

A student:
  • represents data and interprets data displays made from objects

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

    MA1-17SP
  • selects appropriate methods to collect data, and constructs, compares, interprets and evaluates data displays, including tables, picture graphs and column graphs

    MA2-18SP
  • uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots, line graphs and two-way tables

    MA3-18SP
  • collects, represents and interprets single sets of data, using appropriate statistical displays

    MA4-19SP
  • analyses single sets of data using measures of location, and range

    MA4-20SP
  • uses statistical displays to compare sets of data, and evaluates statistical claims made in the media

    MA5.1-12SP
  • uses quartiles and box plots to compare sets of data, and evaluates sources of data

    MA5.2-15SP
  • uses standard deviation to analyse data

    MA5.3-18SP
  • investigates relationships between two statistical variables, including their relationship over time

    MA5.2-16SP
  • investigates the relationship between numerical variables using lines of best fit, and explores how data is used to inform decision-making processes

    MA5.3-19SP
  • recognises and describes the element of chance in everyday events

    MA1-18SP
  • describes and compares chance events in social and experimental contexts

    MA2-19SP
  • conducts chance experiments and assigns probabilities as values between 0 and 1 to describe their outcomes

    MA3-19SP
  • represents probabilities of simple and compound events

    MA4-21SP
  • calculates relative frequencies to estimate probabilities of simple and compound events

    MA5.1-13SP
  • describes and calculates probabilities in multi-step chance experiments

    MA5.2-17SP