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Working MathematicallyStudents: 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

Communicating: uses appropriate terminology to describe, and symbols to represent, mathematical ideas MA2-1WM Problem Solving: selects and uses appropriate mental or written strategies, or technology, to solve MA2-2WM Reasoning: checks the accuracy of a statement and explains the reasoning used MA2-3WM

Numeracy Continuum

ASPECT 1Forward Number Word Sequence Counts beyond 100Backward Number Word Sequence Counts backwards from any numberNumeral identification Identifies numerals in the range 1-10000Counting By 10s and 100s Counts forwards and backwards by 100s, off the 100, and on or off the decade to 1000, eg. 24, 124, 224,.....924ASPECT 3Number Properties Understands the structural properties of numbers including how to regroup when operating with numbers. For example, 9x6=6x6+3x6, 27+38+3=(27+3)+38ASPECT 4Tens and Ones2a: Jump Method Treats ten as a unit that can be repeatedly constructed in place of ten individual counts. Tens and ones are flexibly regrouped. Counts forwards or backwards firstly by tens and then by ones2b: Split Method Treats ten as an abstract composite unit Solves addition and subtraction problems mentally by separating the tens from the ones, then adding or subtracting each separately before combining Uses non-standard decomposition of two-digit numbers, eg, 76=60+16Hundreds, Tens and Ones3a: Jump Method Uses hundreds, tens and ones in standard decomposition, eg. 326 as three groups of 100, two groups of 10 and six ones Increments by hundreds and tens to add mentally Determines the number of tens in 621 without counting by ten

Number and Algebra - Students: Develop efficient strategies for numerical calculation, recognise patterns, describe relationships and apply algebraic techniques and generalisation Te

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Whole Number

MA2-4NA applies place value to order, read and represent numbers of up to five digitsRecognise, model, represent and order numbers to at least 10 000 ACMNA052Represent numbers of up to four digits using objects, words, numerals and digital displays Make the largest and smallest number from four given digits Identify the number before and after a given two-, three- or four-digit numberDescribe the number before as 'one less than' and the number after as 'one more than' a given numberCount forwards and backwards by tens and hundreds on and off the decadeArrange numbers of up to four digits in ascending and descending orderUse place value to compare and explain the relative size of four-digit numbers Use the terms and symbols for 'is less than' and 'is greater than' to show the relationship between two numbers Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems ACMNA053

Apply an understanding of place value and the role of zero to read, write and order numbers of up to four digits Interpret four-digit numbers used in everyday contexts Use place value to partition numbers of up to four digitsState the 'place value' of digits in numbers of up to four digitsRecord numbers of up to four digits using place valuePartition numbers of up to four digits in non-standard forms Round numbers to the nearest ten, hundred or thousand

Working Mathematically

Maths Checklist Stage 2 - Year 3

Language: plus, add, addition, minus, the difference between, subtract, subtraction, equals, is equal to, is the same as, number sentence, empty number line, strategy, digit, estimate, round to.

Language: number before, number after, more than, greater than, less than, largest number, smallest number, ascending order, descending order, digit, zero, ones, groups of ten, tens, groups of one hundred, hundreds, groups of one thousand, thousands, place value, round to.


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Addition and Subtraction

MA2-5NA uses mental and written strategies for addition and subtraction involving two-, three-, four- and five-digit numbersRecall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation ACMNA055

Add three or more single-digit numbersModel and apply the associative property of addition to aid mental computationApply known single-digit addition and subtraction facts to mental strategies for addition and subtraction of two-, three- and four-digit numbers, including: − the jump strategy on an empty number line− the split strategy− the compensation strategy− using patterns to extend number facts− bridging the decades− changing the order of addends to form multiples of 10− using place value to partition numbers− partitioning numbers in non-standard formsChoose and apply efficient strategies for addition and subtraction Discuss and compare different methods of addition and subtraction Use concrete materials to model the addition and subtraction of two or more numbers, with and without trading, and record the method usedSelect, use and record a variety of mental strategies to solve addition and subtraction problems, including word problems, with numbers of up to four digits Give a reasonable estimate for a problem, explain how the estimate was obtained, and check the solution Use the equals sign to record equivalent number sentences involving addition and subtraction and so to mean 'is the same as', rather than to mean to perform an operationCheck given number sentences to determine if they are true or false and explain why

Recognise and explain the connection between addition and subtraction ACMNA054

Demonstrate how addition and subtraction are inverse operationsExplain and check solutions to problems, including by using the inverse operation Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents ACMNA059

Calculate equivalent amounts of money using different denominationsPerform simple calculations with money, including finding change, and round to the nearest five centsCalculate mentally to give change

Numeracy Continuum

3b: Split Method Adds and subtracts mentally combinations of numbers to 1000 Uses the positional value of numbers flexibly in regrouping without the need to rely on incrementing by tens or hundreds Uses a part-whole knowledge of numbers to 100

ASPECT 5Multiplication and Division as Operations Coordinates two composite units as an operation, eg. 6 times 3 is 18; 18÷6=3 Uses multiplication and division as inverse operations flexibly in problem solving tasks

ASPECT 6Equal Partitions Verifies continuous and discrete linear arrangements have been partitioned into thirds or fifths by iterating one part to form the whole or checking the equality and number of parts forming the whole

ASPECT 7Iterates the unit Uses a single unit repeatedly (iterating) to measure or construct length Make a multi-unit ruler by iterating a single unit and quantifying accumulated distance Identifies the quantitative relationship between length and number of units (ie. If you halve the size of the units you will have twice as many units to measure)Composite Area Creates the row-column structure of the iterated composite unit of area Uses the row-column structure to find the number of units to measure area

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 reasoningCommunicating: uses appropriate terminology to describe, and symbols to represent, mathematical ideas MA2-1WM Problem Solving: selects and uses appropriate mental or written strategies, or technology, to solve MA2-2WM Reasoning: checks the accuracy of a statement and explains the reasoning used MA2-3WM




Numeracy Continuum

Working MathematicallyStudents: Develop understanding and fluency in mathematics through inquiry, exploring and connecting mathematical concepts, choosing and applying problem-solving skills and mathematical techniques, communication and reasoningCommunicating: uses appropriate terminology to describe, and symbols to represent, mathematical ideas MA2-1WM Problem Solving: selects and uses appropriate mental or written strategies, or technology, to solve MA2-2WM Reasoning: checks the accuracy of a statement and explains the reasoning used MA2-3WM


Language: group, row, column, horizontal, vertical, array, multiply, multiplied by, multiplication, multiplication facts, double, shared between, divide, divided by, division, equals, strategy, digit, number chart.


Language: whole, part, equal parts, half, quarter,eighth, third, fifth, one-third, one-fifth, fraction, denominator, numerator, mixed numeral, whole number,


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Multiplication and Division

MA2-6NA uses mental and informal written strategies for multiplication and divisionRecall multiplication facts of two, three, five and ten and related division facts ACMNA056

Count by twos, threes, fives or tens using skip countingUse mental strategies to recall multiplication facts for multiples of two, three, five and tenRelate 'doubling' to multiplication facts for multiples of twoRecognise and use the symbols for multiplied by (×), divided by (÷) and equals (=) Link multiplication and division facts using groups or arraysExplain why a rectangular array can be read as a division in two ways by forming vertical or horizontal groupsModel and apply the commutative property of multiplicationRepresent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies ACMNA057

Use mental strategies to multiply a one-digit number by a multiple of 10, including: − repeated addition− using place value concepts− factorising the multiple of 10Apply the inverse relationship of multiplication and division to justify answersSelect, use and record a variety of mental strategies, and appropriate digital technologies, to solve simple multiplication problemsPose multiplication problems and apply appropriate strategies to solve them Explain how an answer was obtained and compare their own method of solution with the methods of other students Explain problem-solving strategies using language, actions, materials and drawings Describe methods used in solving multiplication problems





Numeracy Continuum


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Fractions and Decimals

MA2-7NA represents, models and compares commonly used fractions and decimalsModel and represent unit fractions, including and their multiples, to a complete whole ACMNA058

Model fractions with denominators of 2, 3, 4, 5 and 8 of whole objects, shapes and collections using concrete materials and diagramsRecognise that as the number of parts that a whole is divided into becomes larger, the size of each part becomes smaller Recognise that fractions are used to describe one or more parts of a whole where the parts are equalName fractions up to one wholeInterpret the denominator as the number of equal parts a whole has been divided intoInterpret the numerator as the number of equal fractional partsUse the terms 'fraction', 'denominator' and 'numerator' appropriately when referring to fractionsCount by quarters, halves and thirds, including with mixed numerals; locate and represent these fractions on a number line ACMNA078Identify and describe 'mixed numerals' as having a whole-number part and a fractional part

Rename and as 1Count by halves, thirds and quarters, Place halves, quarters, eighths and thirds on number lines between 0 and 1, Place halves, thirds and quarters on number lines that extend beyond 1Compare unit fractions using diagrams and number lines and by referring to the denominatorRecognise and explain the relationship between the value of a unit fraction and its denominator

Numeracy Continuum





Language: pattern, goes up by, goes down by, even, odd, rows, digit, multiplication facts.


Language: length, distance, metre, centimetre,millimetre, ruler, measure, estimate, handspan.


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Patterns and Algebra

MA2-8NA generalises properties of odd and even numbers, generates number patterns, and completes simple number sentences by calculating missing valuesDescribe, continue and create number patterns resulting from performing addition or subtraction ACMNA060

Identify and describe patterns when counting forwards or backwards by threes, fours, sixes, sevens, eights and nines from any starting pointModel, describe and then record number patterns using diagrams, words or symbols Ask questions about how number patterns have been created and how they can be continuedCreate and continue a variety of number patterns that increase or decrease, and describe them in more than one way Investigate the conditions required for a number to be even or odd and identify even and odd numbers ACMNA051

Model even and odd numbers of up to two digits using arrays with two rowsCompare and describe the difference between models of even numbers and models of odd numbersRecognise the connection between even numbers and the multiplication facts for two Describe and generalise the conditions for a number to be even or oddRecognise the significance of the final digit of a whole number in determining whether a given number is even or odd Identify even or odd numbers of up to four digits

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 Te

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Length

MA2-9MG measures, records, compares and estimates lengths, distances and perimeters in metres, centimetres and millimetres, and measures, compares and records temperaturesMeasure, order and compare objects using familiar metric units of length ACMMG061

Measure lengths and distances using metres and centimetresRecord lengths and distances using metres and centimetres Compare and order lengths and distances using metres and centimetresEstimate lengths and distances using metres and centimetres and check by measuringExplain strategies used to estimate lengths and distances, such as by referring to a known length Recognise the need for a formal unit smaller than the centimetre to measure lengthRecognise that there are 10 millimetres in one centimetre, ie 10 millimetres = 1 centimetreUse the millimetre as a unit to measure lengths to the nearest millimetre, using a rulerDescribe how a length or distance was measured Record lengths using the abbreviation for millimetres (mm)Estimate lengths to the nearest millimetre and check by measuring

Numeracy Continuum






Language: area, surface, measure, grid, row, column, square centimetre, square metre, estimate.

Numeracy Continuum


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AreaMA2-10MG measures, records, compares and estimates areas using square centimetres and square metresRecognise and use formal units to measure and estimate the areas of rectanglesRecognise the need for the square centimetre as a formal unit to measure areaUse a 10 cm × 10 cm tile (or grid) to find the areas of rectangles (including squares) that are less than, greater than or about the same as 100 square centimetresMeasure the areas of rectangles (including squares) in square centimetresUse efficient strategies for counting large numbers of square centimetresRecord area in square centimetres using words and the abbreviation for square centimetres (cm2)Estimate the areas of rectangles (including squares) in square centimetresDiscuss strategies used to estimate area in square centimetresRecognise the need for a formal unit larger than the square centimetre to measure areaConstruct a square metre and use it to measure the areas of large rectangles (including squares)Recognise areas that are 'less than a square metre', 'about the same as a square metre' and 'greater than a square metre'Recognise that an area of one square metre need not be a squareRecord areas in square metres using words and the abbreviation for square metres (m2)Estimate the areas of rectangles (including squares) in square metresDiscuss strategies used to estimate area in square metres



Language: capacity, container, litre, volume, layers, cubic centimetre, measure, estimate.


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Volume and Capacity

MA2-11MG measures, records, compares and estimates volumes and capacities using litres, millilitres and cubic centimetresMeasure, order and compare objects using familiar metric units of capacity ACMMG061

Recognise the need for formal units to measure volume and capacityExplain the need for formal units to measure volume and capacity Use the litre as a unit to measure volumes and capacities to the nearest litreRelate the litre to familiar everyday containersRecognise that one-litre containers can be a variety of shapesRecord volumes and capacities using the abbreviation for litres (L) Compare and order two or more containers by capacity measured in litresEstimate the capacity of a container in litres and check by measuringEstimate the number of cups needed to fill a container with a capacity of one litre Compare objects using familiar metric units of volume ACMMG290

Recognise the advantages of using a cube as a unit when packing and stackingUse the cubic centimetre as a unit to measure volumesPack small containers with cubic-centimetre blocks and describe packing in terms of layersConstruct three-dimensional objects using cubic-centimetre blocks and count the blocks to determine the volumes of the objectsDevise and explain strategies for counting blocksRecord volumes using the abbreviation for cubic centimetres Compare the volumes of two or more objects made from cubic-centimetre blocks by counting blocksDistinguish between mass and volume





Numeracy Continuum



Numeracy Continuum



Language: mass, more than, less than, about the same as, pan balance, (level) balance, measure, estimate, kilogram.


Language: time, clock, analog, digital, hour hand, minute hand, second hand, revolution, numeral, hour, minute, second, o'clock, (minutes) past, (minutes) to.


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Mass

MA2-12MG measures, records, compares and estimates the masses of objects using kilograms and gramsMeasure, order and compare objects using familiar metric units of mass ACMMG061

Recognise the need for a formal unit to measure massUse the kilogram as a unit to measure mass, using a pan balanceAssociate kilogram measures with familiar objectsRecognise that objects with a mass of one kilogram can be a variety of shapes and sizes Record masses using the abbreviation for kilograms (kg) Use hefting to identify objects that have a mass of 'more than', 'less than' and 'about the same as' one kilogramDiscuss strategies used to estimate massCompare and order two or more objects by mass measured to the nearest kilogramEstimate the number of similar objects that have a total mass of one kilogram and check by measuringExplain why two students may obtain different measures for the same mass





Numeracy Continuum


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Time

MA2-13MG reads and records time in one-minute intervals and converts between hours, minutes and secondsTell time to the minute and investigate the relationship between units of time ACMMG062

Recognise the coordinated movements of the hands on an analog clock, including:− the number of minutes it takes for the minute hand to move from one numeral to the next− the number of minutes it takes for the minute hand to complete one revolution− the number of minutes it takes for the hour hand to move from one numeral to the next− the number of minutes it takes for the minute hand to move from the 12 to any other numeral− the number of seconds it takes for the second hand to complete one revolutionRead analog and digital clocks to the minute, including using the terms 'past' and 'to'Record in words various times shown on analog and digital clocks


Language: object, two-dimensional shape (2D shape), three-dimensional object (3D object), cone, cube, cylinder, prism, pyramid, sphere, surface, flat surface, curved surface, face, edge,


Numeracy Continuum


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Three Dimensional SpaceMA2-14MG makes, compares, sketches and names three-dimensional objects, including prisms, pyramids, cylinders, cones and spheres, and describes their featuresMake models of three-dimensional objects and describe key features ACMMG063

Identify and name three-dimensional objects as prisms (including cubes), pyramids, cylinders, cones and spheres Recognise and describe the use of three-dimensional objects in a variety of contextsDescribe and compare curved surfaces and flat surfaces of cylinders, cones and spheres, and faces, edges and vertices of prisms (including cubes) and pyramids Describe similarities and differences between prisms (including cubes), pyramids, cylinders, cones and spheres Use a variety of materials to make models of prisms (including cubes), pyramids, cylinders, cones and spheres, given a three-dimensional object, picture or photograph to viewDeconstruct everyday packages that are prisms (including cubes) to create netsRecognise that a net requires each face to be connected to at least one other face Investigate, make and identify the variety of nets that can be used to create a particular prism, such as the variety of nets that can be used to make a cubeDistinguish between (flat) nets, which are 'two-dimensional', and objects created from nets, which are 'three-dimensional'

Language: shape, two-dimensional shape (2D shape), circle, triangle, quadrilateral, parallelogram, rectangle, rhombus, square, trapezium, kite, pentagon, hexagon, octagon, regular shape, irregular shape, orientation, features, properties, side, parallel, pair of parallel sides, opposite, length, vertex (vertices), angle, right angle, symmetry, line (axis) of symmetry, rigid.

Language: object, two-dimensional shape (2D shape), three-dimensional object (3D object), cone, cube, cylinder, prism, pyramid, sphere, surface, flat surface, curved surface, face, edge,





Numeracy Continuum


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Two Dimensional Space

MA2-15MG manipulates, identifies and sketches two-dimensional shapes, including special quadrilaterals, and describes their featuresCompare and describe features of two-dimensional shapes, including the special quadrilateralsManipulate, compare and describe features of two-dimensional shapes, including the special quadrilaterals: parallelograms, rectangles, rhombuses, squares, trapeziums and kites Determine the number of pairs of parallel sides, if any, of each of the special quadrilateralsUse measurement to establish and describe side properties of the special quadrilateralsIdentify and name the special quadrilaterals presented in different orientationsExplain why a particular quadrilateral has a given nameName a shape, given a written or verbal description of its features Recognise the vertices of two-dimensional shapes as the vertices of angles that have the sides of the shape as their arms Identify right angles in squares and rectanglesGroup parallelograms, rectangles, rhombuses, squares, trapeziums and kites using one or more attributesIdentify and describe two-dimensional shapes as either 'regular' or 'irregular'Identify regular shapes in a group that includes irregular shapes, such as a regular pentagon in a group of pentagons,Explain the difference between regular and irregular two-dimensional shapesRecognise that the name of a shape does not change if its size or orientation in space is changedDraw representations of regular and irregular two-dimensional shapes in different orientationsConstruct regular and irregular two-dimensional shapes from a variety of materialsDetermine that a triangle cannot be constructed from three straws if the sum of the lengths of the two shorter straws is less than the length of the longest straw Compare the rigidity of two-dimensional frames of three sides with the rigidity of those of four or more sidesConstruct and manipulate a four-sided frame and explain how adding a brace can make a four-sided frame rigid Identify symmetry in the environment ACMMG066

Identify lines of symmetry in pictures, artefacts, designs and the environmentIdentify and draw lines of symmetry on given shapes, including the special quadrilaterals and other regular and irregular shapes Determine and explain whether a given line through a shape is a line of symmetry Recognise and explain why any line through the centre of (and across) a circle is a line of symmetry

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 reasoningCommunicating: uses appropriate terminology to describe, and symbols to represent, mathematical ideas MA2-1WM Problem Solving: selects and uses appropriate mental or written strategies, or technology, to solve MA2-2WM Reasoning: checks the accuracy of a statement and explains the reasoning used MA2-3WM

Language: shape, circle, triangle, square, rectangle, features, side, straight line, curved line, open line, closed shape




Numeracy Continuum


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Angles

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

Identify angles as measures of turn and compare angle sizes in everyday situations ACMMG064

Identify 'angles' with two arms in practical situationsIdentify the 'arms' and 'vertex' of an angle Describe informally an angle as the 'amount of turning' between two armsRecognise that the length of the arms does not affect the size of the angle Compare angles directly by placing one angle on top of another and aligning one armIdentify 'perpendicular' lines in pictures, designs and the environment Use the term 'right angle' to describe the angle formed when perpendicular lines meet Describe examples of right angles in the environment Identify right angles in two-dimensional shapes and three-dimensional objects

Statistics and ProbabilityStudents - collect, represent, analyse, interpret and evaluate data, assign and use probabilities, and make sound judgments

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Position

MA2-17MG uses simple maps and grids to represent position and follow routes, including using compass directionsCreate and interpret simple grid maps to show position and pathways ACMMG065

Describe the location of an object using more than one descriptorUse given directions to follow routes on simple maps Use and follow positional and directional language Use grid references on maps to describe positionUse grid references in games Identify and mark particular locations on maps and plans, given their grid referencesDraw and label a grid on a given mapDiscuss the use of grids in real-world contexts Draw simple maps and plans from an aerial view, with and without labelling a grid Create simple maps and plans using digital technologies Compare different methods of identifying locations in the environmentDraw and describe routes or paths on grid-referenced maps and plans Use digital technologies involving maps, position and paths Interpret and use simple maps found in factual texts and in the media


Language: position, location, map, plan, path,route, grid, grid reference, aerial view, directions.





Numeracy Continuum


Language: information, data, collect, category, display, symbol, list, table, column graph, picture graph, vertical columns, horizontal bars, equal spacing, title, key, vertical axis, horizontal axis, axes, spreadsheet.


Numeracy Continuum


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Data

MA2-18SP selects appropriate methods to collect data, and constructs, compares, interprets and evaluates data displays, including tables, pictureIdentify questions or issues for categorical variables; identify data sources and plan methods of data collection and recording ACMSP068Recognise that data can be collected either by the user or by othersIdentify possible sources of data collected by others Pose questions about a matter of interest to obtain information that can be recorded in categoriesPredict and create a list of categories for efficient data collection in relation to a matter of interestIdentify issues for data collection and refine investigationsCollect data, organise it into categories, and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies ACMSP069

Collect data and create a list or table to organise the dataUse computer software to create a table to organise collected dataConstruct vertical and horizontal column graphs and picture graphs that represent data using one-to-one correspondenceUse grid paper to assist in constructing graphs that represent data using one-to-one correspondenceUse the terms 'horizontal axis', 'vertical axis' and 'axes' appropriately when referring to column graphsUse graphing software to enter data and create column graphs that represent data Mark equal spaces on axes, name and label axes, and choose appropriate titles for column graphsChoose an appropriate picture or symbol for a picture graph and state the key used Interpret and compare data displays ACMSP070

Describe and interpret information presented in simple tables, column graphs and picture graphs Make conclusions about data presented in different data displaysRepresent the same data set using more than one type of display and compare the displaysDiscuss the advantages and/or disadvantages of different representations of the same data






Numeracy Continuum


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Chance

MA2-19SP describes and compares chance events in social and experimental contextsConduct chance experiments, identify and describe possible outcomes, and recognise variation in results ACMSP067

Use the term 'outcome' to describe any possible result of a chance experiment Predict and list all possible outcomes in a chance experiment, Predict and record all possible combinations in a chance situationPredict the number of times each outcome should occur in a chance experiment involving a set number of trials, carry out the experiment, and compare the predicted and actual resultsKeep a tally and graph the results of a chance experimentExplain any differences between expected results and actual results in a chance experimentMake statements that acknowledge 'randomness' in a situationRepeat a chance experiment several times and discuss why the results vary

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