overseas- and Australian-born children whose first language is a language other than English Aboriginal and Torres Strait Islander students whose first language is an Indigenous language, including traditional languages Aboriginal and Torres Strait Islander students whose first language is Aboriginal English, including creoles and related varieties. EAL/D learners enter Australian schools at different ages and stages of schooling and at different stages of English language learning. They have diverse talents and capabilities and a range of prior learning experiences and levels of literacy in their first language and in English. EAL/D students represent a significant and growing percentage of learners in NSW schools. For some, school is the only place they use English. EAL/D learners are simultaneously learning a new language and the knowledge, skills and understanding of the Mathematics syllabus through that new language. They require additional time and support, along with informed teaching that explicitly addresses their language needs, and assessments that take into account their developing language proficiency. NATIONAL LITERACY AND NUMERACY LEARNING PROGRESSIONS The can assist in strengthening teacher knowledge and facilitating a shared professional understanding of literacy and numeracy development. The progressions can be used to identify the literacy and numeracy development of students and the development that should follow. This assists teachers to differentiate teaching and learning experiences and to provide feedback to students about next steps in learning. The progressions are used in conjunction with the syllabuses, which remain the focus for planning, programming, teaching, learning and assessment. The progressions are organised into elements and sub-elements that describe common developmental pathways as students become increasingly adept in particular aspects of literacy and numeracy. Each sub-element is clarified by descriptions of observable student behaviours known as indicators. The indicators within each sub-element are grouped together to form developmental levels. The has been mapped to the NSW English K–10 syllabus and the has been mapped to the NSW Mathematics K–10 syllabus to demonstrate the range and level of literacy and numeracy skills required to access the outcomes and content.
MA4-3WM recognises and explains mathematical relationships using reasoning MA5.1-3WM provides reasoning to support conclusions that are appropriate to the context MA5.2-3WM constructs arguments to prove and justify results 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 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 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 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 Fractions and Decimals Fractions and Decimals Fractions, Decimals and Percentages digit
MAe-7NA describes two equal parts as halves MA1-7NA represents and models halves, quarters and eighths MA2-7NA represents, models and compares commonly used fractions and decimals MA3-7NA compares, orders and calculates with fractions, decimals and percentages STAGE 4 STAGE 5.1 STAGE 5.2 STAGE 5.3 Computation with Integers MA4-4NA compares, orders and calculates with integers, applying a range of strategies to aid computation Fractions, Decimals and Percentages MA4-5NA operates with fractions, decimals and percentages Financial Mathematics Financial Mathematics Financial Mathematics ◊
STAGE 4 STAGE 5.1 STAGE 5.2 STAGE 5.3 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 Linear Relationships MA5.1-6NA determines the Linear Relationships ◊ MA5.2-9NA uses the Linear Relationships § MA5.3-8NA uses formulas to
distances using everyday language lengths and distances using uniform informal units, metres and centimetres lengths, distances and perimeters in metres, centimetres and millimetres, and measures, compares and records temperatures device to measure lengths and distances, calculates perimeters, and converts between units of length 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 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 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
STAGE 4 STAGE 5.1 STAGE 5.2 STAGE 5.3 Length MA4-12MG calculates the perimeters of plane shapes and the circumferences of circles 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 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 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
MAe-16MG describes position and gives and follows simple directions using everyday language MA1-16MG represents and describes the positions of objects in everyday situations and on maps MA2-17MG uses simple maps and grids to represent position and follow routes, including using compass directions MA3-17MG locates and describes position on maps using a grid-reference system STAGE 4 STAGE 5.1 STAGE 5.2 STAGE 5.3 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 Angle Relationships MA4-18MG identifies and uses angle relationships, including those related to transversals on sets of parallel lines
3 1 A student: describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions MA31WM gives a valid reason for supporting one possible solution over another MA33WM selects and uses the appropriate unit to estimate, measure and calculate volumes and capacities, and converts between units of capacity MA311MG Students: Choose appropriate units of measurement for volume and capacity (ACMMG108) select and use appropriate units to measure the capacities of a variety of containers, eg millilitres for a drinking glass, litres for a water urn measure the volumes of rectangular containers by packing them with cubic-centimetre blocks explain the advantages and disadvantages of using cubic-centimetre blocks as a unit to measure volume (Communicating, Reasoning) describe arrangements of cubic-centimetre blocks in containers in terms of layers, eg 5 layers of 8 cubic-centimetre blocks (Problem Solving) recognise the need for a formal unit larger than the cubic centimetre construct and use the cubic metre as a unit to measure larger volumes explain why volume is measured in cubic metres in certain situations, eg wood bark, soil, concrete (Communicating, Reasoning) recognise that a cubic metre can have dimensions other than a cube of side 1 metre, eg 2 metres by metre by 1 metre (Problem Solving) record volumes using the abbreviation for cubic metres (m3) estimate the size of a cubic metre, half a cubic metre and two cubic metres select and use appropriate units to estimate the volumes of a variety of objects, eg cubic centimetres for a lolly jar, cubic metres for the classroom Background Information The attribute of volume is the amount of space occupied by an object or substance and is usually measured in cubic units, eg cubic centimetres (cm3) and cubic metres (m3). Capacity refers to the amount a container can hold and is measured in units, such as millilitres (mL), litres (L) and kilolitres (kL). Capacity is only used in relation to containers and generally
Language Students should be able to communicate using the following language: angle, arm, vertex, protractor, degree. National Numeracy Learning Progression links to this Mathematics outcome When working towards the outcome MA316MG the sub-elements (and levels) of Understanding geometric properties (UGP5) describe observable behaviours that can aid teachers in making evidence-based decisions about student development and future learning. The progression sub-elements and indicators can be viewed by accessing the .
4 A student: communicates and connects mathematical ideas using appropriate terminology, diagrams and symbols MA41WM applies appropriate mathematical techniques to solve problems MA42WM performs calculations of time that involve mixed units, and interprets time zones MA415MG Related Life Skills outcomes: MALS-20MG, MALS-21MG, MALS-22MG, MALS-23MG, Students: Solve problems involving duration, including using 12-hour and 24-hour time within a single time zone (ACMMG199) add and subtract time mentally using bridging strategies, eg from 2:45 to 3:00 is 15 minutes and from 3:00 to 5:00 is 2 hours, so the time from 2:45 until 5:00 is 15 minutes + 2 hours = 2 hours 15 minutes add and subtract time with a calculator, including by using the 'degrees, minutes, seconds' button round answers to time calculations to the nearest minute or hour interpret calculator displays for time calculations, eg 2.25 on a calculator display for a time calculation means hours or 2 hours 15 minutes solve a variety of problems involving duration, including where times are expressed in and 24-hour notation, that require the use of mixed units (years, months, days, hours and/or minutes) Solve problems involving international time zones compare times in, and calculate time differences between, major cities of the world, eg 'Given that London is 10 hours behind Sydney, what time is it in London when it is 6:00 pm in Sydney?' interpret and use information related to international time zones from maps (Problem Solving) solve problems involving international time as it relates to everyday life, eg determine whether a particular soccer game can be watched live on television during normal waking hours (Problem Solving)
5.2 ◊ A student: selects appropriate notations and conventions to communicate mathematical ideas and solutions MA5.21WM constructs arguments to prove and justify results MA5.23WM uses the gradient-intercept form to interpret and graph linear relationships MA5.29NA Students: Interpret and graph linear relationships using the gradient-intercept form of the equation of a straight line graph straight lines with equations in the form ('gradient-intercept form') recognise equations of the form as representing straight lines and interpret the xcoefficient as the gradient, and the constant as the yintercept, of a straight line rearrange an equation of a straight line in the form ('general form') to gradient-intercept form to determine the gradient and the yintercept of the line find the equation of a straight line in the form , given the gradient and the yintercept of the line graph equations of the form by using the gradient and the yintercept, and with the use of digital technologies use graphing software to graph a variety of equations of straight lines, and describe the similarities and differences between them, eg (Communicating) explain the effect of changing the gradient or the yintercept on the graph of a straight line (Communicating, Reasoning) find the gradient and the yintercept of a straight line from its graph and use these to determine the equation of the line match equations of straight lines to graphs of straight lines and justify choices (Communicating, Reasoning) Solve problems involving parallel and perpendicular lines (ACMNA238) determine that straight lines are perpendicular if the product of their gradients is –1 graph a variety of straight lines, including perpendicular lines, using digital technologies and compare their gradients to establish the condition for lines to be perpendicular (Communicating, Reasoning)
estimate the cost of a range of items and select the appropriate coin or note to pay for the items, eg select a $2 coin to pay for a drink or snack, select a $20 note to pay for a T-shirt, estimate that a $50 note will be needed to pay for a number of items at a supermarket (Communicating, Understanding, Fluency) select additional coins or notes to pay for an item if the original amount tendered was not sufficient (Reasoning, Understanding) calculate the amount of change due in relation to a transaction for goods or services, using mental strategies, written processes and/or calculator strategies calculate the change to be given when purchasing an item, eg calculate the change to be given when purchasing a $2.50 magazine with a $5 note and count the coins received in change (Problem Solving, Reasoning) estimate the amount of change due in relation to a transaction for goods or services estimate the amount of change due for a purchase and check using a calculator, eg the change due following a purchase of $3.50 if a $5 note is tendered (Problem Solving, Reasoning)
variable (statistics) A variable is something measurable or observable that is expected to change either over time or between individual observations. Examples of variables in statistics include the age of students, their hair colour or a playing field's length or its shape. Venn diagram A Venn diagram is a graphical representation of the extent to which two or more events, for example and , are mutually inclusive (overlap) or mutually exclusive (do not overlap). vertically opposite angle When two lines intersect, four angles are formed at the point of intersection. In the diagram, the angles marked AOX and BOY are called vertically opposite. volume The volume of a solid region is a measure of the size of a region. For a rectangular prism, . whole number A whole number is a non-negative integer, that is, one of the numbers 0, 1, 2, 3, … Sometimes it is taken to mean only a positive integer, or any integer.