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• VC2M4N06

  develop efficient mental and written strategies and use appropriate digital tools for solving problems involving addition and subtraction, and multiplication and division where there is no remainder

  Elaborations

  • using and choosing efficient calculation strategies for addition and subtraction problems involving larger numbers, for example, place value partitioning, inverse relationship, compatible numbers, jump strategies, bridging tens, splitting one or more numbers, extensions to basic facts, algorithms and digital tools where appropriate
  • using physical or virtual materials to demonstrate doubling and halving strategies for solving multiplication problems; for example, for 5 × 18, using the fact that double 5 is 10 and half of 18 is 9; or using 10 × 18 = 180, then halving 180 to get 90; or applying the associative property of multiplication, where 5 × 18 becomes 5 × 2 × 9, then 5 × 2 × 9 = 10 × 9 = 90 so that 5 × 18 = 90
  • using an array to represent a multiplication problem, connecting the idea of how many groups and how many in each group with the rows and columns of the array, and writing an associated number sentence
  • using materials or a diagram to solve a multiplication or division problem, by writing a number sentence and explaining what each of the numbers within the number sentence refers to
  • representing a multiplicative situation using materials, array diagrams and/or a bar model, and writing multiplication and/or division number sentences, based on whether the number of groups, the number per group or the total is missing, and explaining how each number in their number sentence is connected to the situation
  • using place value partitioning, basic facts and an area or region model to represent and solve multiplication problems; for example, for 16 × 4, thinking 10 × 4 and 6 × 4, then 40 + 24 = 64, or a double double strategy where double 16 is 32, double this is 64, so 16 × 4 is 64

  VC2M4N06 | Mathematics | Mathematics Version 2.0 | Level 4 | Number

• VC2M7ST02

  create different types of displays of numerical data, including dot plots and stem-and-leaf plots, using software where appropriate; describe and compare the distribution of data, commenting on the shape, centre and spread including outliers and determining the range, median, mean and mode

  Elaborations

  • using ordered stem-and-leaf plots to record and display numerical data collected in a class investigation, such as constructing a class plot of height in centimetres on a shared stem-and-leaf plot for which the stems 12, 13, 14, 15, 16 and 17 have been produced
  • comparing variation in attributes by category using split stem-and-leaf plots or dot plots; interpreting the shape of the distribution using qualitative terms to describe ‘symmetry’, ‘skewness’ and ‘average’ in terms of the mean, median and mode, and the amount of variation based on qualitative descriptions of the spread of the data
  • connecting features of the data display (for example, highest frequency, clusters, gaps, symmetry or skewness) to the mode, range and median, and the question in context; describing the shape of distributions using terms such as ‘positive skew’, ‘negative skew’, ‘symmetric’ and ‘bi-modal’ and discussing the location of the median and mean on these distributions
  • using mean and median to compare data sets, identifying possible outliers and explaining how these may affect the comparison; recognising how different displays make specific information about data more evident, including proportions, and measures of mean, mode or median, spread and extreme values; understanding that the median and the mean will be the same or similar for symmetric distributions but different for distributions that are skewed
  • comparing the mean and median of data with and without extremes; for example, estimation of standard measures for length or mass, informally considering for a given set of data what might constitute an unexpected, unusual or extreme data value

  VC2M7ST02 | Mathematics | Mathematics Version 2.0 | Level 7 | Statistics

• VC2M4M02

  recognise ways of measuring and approximating the perimeter and area of shapes and enclosed spaces, using appropriate formal and informal units

  Elaborations

  • recognising that perimeter is the sum of the lengths that form the boundary of a shape or enclosed space; choosing suitable units from a range of objects to measure around the boundary of a shape such as a garden bed; comparing the results to say which unit was an appropriate choice for the context; and using a piece of string or rope to measure the perimeter of irregular shapes and enclosed spaces, including those that have curved sections
  • creating a range of rectangles representing ‘paddocks’ on grid paper and establishing different methods of working out the length of the boundary fences; and explaining that the more efficient methods involve adding the side lengths rather than counting squares
  • recognising that area is the space enclosed by the boundary of a shape or the surface of an object; measuring and comparing the area of shapes using an array of paper tiles or mosaic squares, including part units to fill gaps at the edge of the shapes; and comparing the total areas by combining the fractional parts to make whole units
  • demonstrating how to use one unit repeatedly to measure the area of a shape (for example, using one paper square to measure and compare the area of a rectangle and a triangle) and recording and explaining how they used part units to give a more accurate measure, and why they needed to ensure there were no gaps or overlaps
  • investigating the ways Aboriginal and/or Torres Strait Islander ranger groups and other groups measure areas of land to make decisions about fire burns to care for Country/Place

  VC2M4M02 | Mathematics | Mathematics Version 2.0 | Level 4 | Measurement

• VC2M6N08

  approximate numerical solutions to problems involving rational numbers and percentages, using appropriate estimation strategies

  Elaborations

  • using familiar fractions, decimals and percentages to approximate calculations, such as 0.3 of 180 is about 13 of 180, or 52% is about 12
  • choosing appropriate estimation strategies including rounding to the nearest whole number, knowledge of multiples of 2, 5 or 10 and partitioning numbers, in contexts such as measuring or cost per unit
  • recognising the effect of rounding on calculations involving fractions or decimals and saying what numbers the answer will be between
  • recognising the usefulness of estimation to check calculations for contexts such as dividing wood into a number of lengths, calculating cost per unit, reducing a recipe or dividing the cost of dinner for a group into individual amounts
  • verifying solutions by estimating percentages in suitable contexts, such as discounts, using common percentages of 10%, 25%, 30%, 50% and 1%
  • investigating estimation strategies to make decisions about steam cooking in ground ovens by Aboriginal and/or Torres Strait Islander Peoples, including catering for different numbers of people and resources needed for cooking

  VC2M6N08 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• VC2M2M02

  identify common uses and represent halves, quarters and eighths in relation to shapes, objects and events

  Elaborations

  • demonstrating how food items can be cut in halves, quarters or eighths; for example, cutting pizzas, slices, cakes or sandwiches into equal parts by halving, then halving again to form quarters and eighths, ensuring that the parts are equal
  • investigating cup and spoon measures used in cooking and discussing what half or quarter of a cup or tablespoon measure means, and using sand or water to compare these to the full cup and tablespoon measures
  • demonstrating and using halves and quarters in folding activities; for example, folding paper in half and quarters and ensuring that the pieces are the same size
  • recognising that halves and quarters can be used to describe lengths, positions and distances; for example, describing the halfway point in a race or instructing someone to stand halfway between 2 chairs
  • discussing that halves and quarters are used to describe durations of time, including durations of time in sporting events, and what this means; for example, discussing how the sirens used during an Australian Rules football game represent quarter time, half-time and three-quarter time during the game, or recognising and using half an hour or quarter of an hour to describe a duration of time

  VC2M2M02 | Mathematics | Mathematics Version 2.0 | Level 2 | Measurement

• VC2M4N10

  follow and create algorithms involving a sequence of steps and decisions that use addition or multiplication to generate sets of numbers; identify and describe any emerging patterns

  Elaborations

  • creating an algorithm that will generate number sequences involving multiples of one to 10 using digital tools to assist, identifying and explaining emerging patterns, and recognising that number sequences can be extended indefinitely
  • creating a basic flow chart that represents an algorithm that will generate a sequence of numbers using multiplication by a constant term; using a calculator to model and follow the algorithm, and recording the sequence of numbers generated; and checking results and describing any emerging patterns
  • using a multiplication formula in a spreadsheet and the ‘fill down’ function to generate a sequence of numbers (for example, entering the number ‘1’ in the cell A1, using ‘fill down’ to cell A100, entering the formula ‘=A1*4’ in the cell B1 and using the ‘fill down’ function to generate a sequence of 100 numbers) and describing emerging patterns
  • creating an algorithm that will generate number sequences involving multiples of one to 10, using digital tools to assist, identifying and explaining emerging patterns, and recognising that number sequences can be extended indefinitely

  VC2M4N10 | Mathematics | Mathematics Version 2.0 | Level 4 | Number

• VC2MFSP01

  sort, name and create familiar shapes; recognise and describe familiar shapes within objects in the environment, giving reasons

  Elaborations

  • sorting a collection of shapes into groups based on different features, such as the number of sides, colour or size, and describing how they have been sorted
  • creating a picture using a variety of shapes and a range of materials, including objects to trace around, describing the shapes they have created or used and sharing why they chose each shape in their picture
  • creating familiar shapes using groups of people; for example, holding hands and creating a circle
  • recognising and naming shapes that are (close to) rectangles, squares, triangles and circles in component parts of everyday items, for example, on bicycles, toy vehicles or kitchen pantry items
  • describing and naming shapes within objects that can be observed on Country/Place, recreating and sorting into groups based on their shape

  VC2MFSP01 | Mathematics | Mathematics Version 2.0 | Foundation Level | Space

• VC2M10M01

  solve problems involving the surface area and volume of composite objects using appropriate units

  Elaborations

  • determining the volumes and surface areas of composite solids, formed from a range of right prisms and cylinders, by considering the individual solids from which they are constructed
  • estimating the surface area and volume of composite objects in practical contexts
  • using mathematical modelling to provide solutions to problems involving surface area and volume; for example, ascertaining the rainfall that can be saved from a rooftop and the optimal shape and dimensions for rainwater storage based on where it will be located on a property, or determining whether to hire extra freezer space for the amount of ice cream required at a fundraising event for the school or community

  VC2M10M01 | Mathematics | Mathematics Version 2.0 | Level 10 | Measurement

• VC2M4P02

  conduct repeated chance experiments to observe relationships between outcomes in games and other chance situations, and identify and describe the variation in results

  Elaborations

  • playing games such as noughts-and-crosses or First to 20 and deciding if it makes a difference who goes first and whether you can use a particular strategy to increase your chances of winning
  • recording and ordering the outcomes of experiments using different physical or virtual random generators such as coins, dice and a variety of spinners
  • experimenting with tossing 2 coins at the same time, recording and commenting on the chance of outcomes after a number of tosses
  • shuffling a set of cards, drawing a card at random, and recording whether it was a spade, club, diamond or heart, or a picture card or numbered card; and repeating the experiment a number of times and discussing the results

  VC2M4P02 | Mathematics | Mathematics Version 2.0 | Level 4 | Probability

• VC2M6SP02

  locate points in the 4 quadrants of the Cartesian plane; describe changes to the coordinates when a point is moved to a different position in the plane

  Elaborations

  • understanding that the Cartesian plane provides a graphical or visual way of describing location with respect to a fixed origin
  • understanding that the axes are number lines that can have different scales, including fractions and decimals, depending on purpose
  • understanding that the horizontal coordinate is written first and is changed if there is a move to the left or right, whereas a move up or down will change the vertical coordinate
  • using the Cartesian plane to draw lines and polygons, listing coordinates in the correct order to complete a polygon
  • investigating and connecting land or star maps used by Aboriginal and Torres Strait Islander Peoples with the Cartesian plane through a graphical or visual way of describing location

  VC2M6SP02 | Mathematics | Mathematics Version 2.0 | Level 6 | Space

• VC2M8N04

  use the 4 operations with integers and with rational numbers, choosing and using efficient mental and written strategies, and digital tools where appropriate, and making estimates for these computations

  Elaborations

  • using patterns to assist in establishing the rules for the multiplication and division of integers
  • applying and explaining efficient strategies such as using the commutative or associative property for regrouping, partitioning, place value, patterning, multiplication or division facts to solve problems involving positive and negative integers, fractions and decimals
  • recognising the effect of sign in the multiplication of integers, for example, (-1)4=1 and (-1)5=-1

  VC2M8N04 | Mathematics | Mathematics Version 2.0 | Level 8 | Number

• VC2M1ST02

  represent collected data for a categorical variable using one-to-one displays and digital tools where appropriate; compare the data using frequencies and discuss the findings

  Elaborations

  • creating a pictograph with objects or drawings; discussing the possible categories for the pictograph, arranging the objects or drawings into the categories; and then reflecting on the chosen categories and deciding whether they were helpful
  • translating data from a list or pictorial display into a tally chart to make counting easier; describing what the tally chart is showing, by referring to the categories; using skip counting by fives to compare the numbers within each category; and explaining how the tally chart answers the question
  • recognising that when there is no data for a particular category you may choose whether or not to include it in your data display, and you may use a zero or blank for that category depending on the purpose of the data collection or presentation; for example, creating a birthday calendar for the class and discussing that there are no students born in May and therefore there are no names listed
  • representing data with objects and drawings where one object or drawing represents one data value, and describing the displays and explaining patterns that have been created using counting strategies to determine the frequency of responses
  • exploring Aboriginal and/or Torres Strait Islander children’s instructive games, for example, Kolap from Mer Island in the Torres Strait region, recording the outcomes, and representing and discussing the results

  VC2M1ST02 | Mathematics | Mathematics Version 2.0 | Level 1 | Statistics

• VC2M2A01

  recognise, describe and create additive patterns that increase or decrease by a constant amount, using numbers, shapes and objects, and identify missing elements in the pattern

  Elaborations

  • creating a pattern sequence with materials, writing the associated number sequence, and then describing the sequence so someone else can replicate it with different materials; for example, using matchsticks or toothpicks to create a growing pattern of triangles – using 3 for one triangle, 5 for 2 triangles, 7 for 3 triangles – and describing the pattern as ‘Start with 3 and add 2 each time’
  • recognising patterns in the built environment to locate additive pattern sequences (for example, responding to ‘How many windows in one train carriage, 2 train carriages, 3 train carriages …?’ or ‘How many wheels on one car, 2 cars, 3 cars …?’) and recording the results in a diagram or table
  • recognising the constant term being added or subtracted in an additive pattern and using it to identify missing elements in the sequence
  • recognising additive patterns in the environment on Country/Place and in Aboriginal and/or Torres Strait Islander material culture; and representing these patterns using drawings, coloured counters and numbers

  VC2M2A01 | Mathematics | Mathematics Version 2.0 | Level 2 | Algebra

• VC2M2A02

  recall and demonstrate proficiency with addition facts to 20; extend and apply facts to develop related subtraction facts

  Elaborations

  • using ten-frames or materials such as connecting cubes to develop and record addition and subtraction strategies including doubles, near doubles, counting on, combinations to 10 and bridging to 10, explaining patterns and connections noticed within the facts
  • partitioning and rearranging collections to practise and develop fluency with addition and subtraction facts to 20, leading to the recall of these facts; for example, partitioning using materials and part-part-whole diagrams to develop subtraction facts related to addition facts, such as 8 + 7 = 15 therefore 15 − 7 = 8 and 15 − 8 = 7
  • using partitioning to develop and record facts systematically (for example, ‘How many ways can 10 birds be spread among 2 trees?’, 10 = 10 + 0, 10 = 9 + 1, 10 = 8 + 2, 10 = 7 + 3, …), explaining how they know they have found all possible partitions 

  VC2M2A02 | Mathematics | Mathematics Version 2.0 | Level 2 | Algebra

• VC2M3A02

  extend and apply knowledge of addition and subtraction facts to 20 to develop efficient mental strategies for computation with larger numbers without a calculator

  Elaborations

  • partitioning using materials and part-part-whole diagrams to develop subtraction facts related to addition facts, such as 8 + 7 = 15 therefore 15 − 7 = 8 and 15 − 8 = 7
  • using partitioning to develop and record facts systematically (for example, ‘How many ways can 12 monkeys be spread among 2 trees?’, 12 = 12 + 0, 12 = 11 + 1, 12 = 10 + 2, 12 = 9 + 3, …), explaining how they know they have found all possible partitions
  • understanding basic addition and related subtraction facts and using extensions to these facts; for example, 6 + 6 = 12, 16 + 6 = 22, 6 + 7 = 13, 16 + 7 = 23, and 60 + 60 = 120, 600 + 600 = 1200

  VC2M3A02 | Mathematics | Mathematics Version 2.0 | Level 3 | Algebra

• VC2M2A03

  recall and demonstrate proficiency with multiplication facts for twos; extend and apply facts to develop the related division facts using doubling and halving

  Elaborations

  • recognising and relating terms such as ‘double’, ‘twice’ and ‘multiply by 2’, and ‘halve’ and ‘divide by 2’ using physical and virtual materials; for example, colouring numbers on a hundreds chart to represent doubles and using it to recognise halves or recognising the doubling pattern and applying the pattern to find related facts such as ‘For 8 twos, think 2 eights’
  • doubling and halving collections to practise and develop fluency with multiplication and division facts for twos, leading to recall of these facts
  • establishing an understanding of doubles and near doubles using physical or virtual manipulatives; for example, using manipulatives to establish that doubling 5 gives you 10, then extending this doubling fact to respond to the question ‘How can you use this fact to double 6 or double 4?’
  • developing fluency with doubling and halving numbers within 20 using physical or virtual materials and playing doubling and halving games; for example, using a physical or virtual dice and choosing whether to double or halve to reach a target number 

  VC2M2A03 | Mathematics | Mathematics Version 2.0 | Level 2 | Algebra

• VC2MFA01

  follow a short sequence of instructions; recognise, copy, continue and create repeating patterns represented in different ways

  Elaborations

  • carrying out a specified sequence of actions to move an object from one location to another
  • playing a simple rule-based game, moving a specified number of places according to the result on a dice in a chance-based game
  • recognising, copying and describing different repeating patterns using materials, shapes, sounds and movements during activities and play; for example, making a bead necklace and describing the pattern they have created, such as ‘red, blue, green, red, blue, green, red, blue, green’, or copying repeating patterns of drumbeats or dance moves during music activities
  • recognising repeating patterns used at home and in daily activities to help make tasks easier or to solve problems; for example, setting the table to eat
  • recognising and describing repeating patterns that can be observed on Country/Place and in Aboriginal and Torres Strait Islander artwork, cultural performances and material cultures, for example, shell and seed necklaces, dances and songs

  VC2MFA01 | Mathematics | Mathematics Version 2.0 | Foundation Level | Algebra

• VC2M9M05

  use mathematical modelling to solve practical problems involving direct proportion, rates, ratio and scale, including financial contexts; formulate the problems and interpret solutions in terms of the situation; evaluate the model and report methods and findings

  Elaborations

  • modelling situations that involve direct proportion (such as pro rata pay rates, exchange rates, multiple quotes for a job, conversion between scales or other appropriate science contexts); for example, situations that involve Hooke’s law and other science contexts involving wavelengths and frequencies
  • modelling situations that impact on image editing used in social media and how proportion may not be maintained and can result in distorted images
  • modelling situations involving compliance with building and construction standards in design and construction, such as the rise and tread of staircases, and vertical and horizontal components of escalators
  • modelling situations involving the application of rates in practical contexts, for example, density, birth, flow or heartbeats
  • exploring fire techniques in land management practices used by Aboriginal and Torres Strait Islander Peoples that use proportion relationships, including the rate of fire spread in different fuel types to wind speed, temperature and relative humidity

  VC2M9M05 | Mathematics | Mathematics Version 2.0 | Level 9 | Measurement

• VC2M8M02

  solve problems involving the volume and capacity of right prisms using appropriate units

  Elaborations

  • using models to demonstrate the number of cubic centimetres in a cubic metre and relating this to capacities of millilitres and litres, recognising that one millilitre is equivalent to one cm³
  • solving practical problems involving volume and capacity, for example, optimal packaging and production
  • choosing which measurements are useful to consider when solving practical problems in context; for example, when purchasing a new washing machine, the dimensions are useful when determining whether it will fit in the available space in the laundry and its capacity is useful when considering the maximum washing load it can carry
  • investigating, reasoning and finding solutions to measurement problems involving dimensions, rates, volume and capacity of objects; for example, given the dimensions of a pool and the rate of flow from a tap, determining how long it will take to fill the pool to its normal capacity

  VC2M8M02 | Mathematics | Mathematics Version 2.0 | Level 8 | Measurement

• VC2M3N01

  identify, explain and use the properties of odd and even numbers

  Elaborations

  • identifying even numbers using skip counting by twos or by grouping even collections of objects in twos
  • explaining why all numbers that end in the digits 0, 2, 4, 6 and 8 are even and that numbers ending in 1, 3, 5, 7 and 9 are odd
  • explaining why some materials can be shared evenly between 2 people without leaving a remainder and some cannot
  • explaining the patterns involved in adding, subtracting and multiplying odd and even numbers (for example, even + even = even, odd + even = odd, odd + odd = even) and using this to decide whether answers to addition, subtraction and multiplication calculations are correct or not
  • following an algorithm consisting of a flow chart with a series of instructions and decisions to determine whether a number is even or odd; and using the algorithm to identify which elements of a set of numbers are divisible by 2

  VC2M3N01 | Mathematics | Mathematics Version 2.0 | Level 3 | Number