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• VC2M5SP03

  describe and perform translations, reflections and rotations of shapes, using dynamic geometry software where appropriate; recognise what changes and what remains the same, and identify any symmetries

  Elaborations

  • understanding and explaining that translations, rotations and reflections can change the position and orientation of a shape but not its shape or size
  • using pattern blocks and paper, tracing around a shape and then conducting a series of one-step transformations and tracing each resulting image, and then finally copying the original position and end position on a new sheet of paper
  • demonstrating how different combinations of transformations can produce the same resulting image
  • challenging classmates to select a combination of transformations to move from an original image to the final image, noting the different combinations by using different colours to trace images
  • investigating how animal tracks can be interpreted by Aboriginal and Torres Strait Islander Peoples using the transformation of their shapes, to help determine and understand animal behaviour

  VC2M5SP03 | Mathematics | Mathematics Version 2.0 | Level 5 | Space

• VC2M4ST01

  acquire data for categorical and discrete numerical variables to address a question of interest or purpose using digital tools; represent data using many-to-one pictographs, column graphs and other displays or visualisations; interpret and discuss the information that has been created

  Elaborations

  • investigating many-to-one data displays using digital tools and graphical software, interpreting and discussing key features
  • understanding that data can be represented with one symbol representing more than one piece of data, and that it is important to read all information about a representation before making judgements
  • constructing graphs of data collected through observation during science experiments, recording, interpreting and discussing the results in terms of the scientific study
  • acquiring samples of data using practical activities, observations or repeated chance experiments; recording data using tally charts, digital tables or spreadsheets; and graphing, discussing and comparing the results using a column graph
  • using secondary data of fire burns to construct data displays that assist Aboriginal and/or Torres Strait Islander ranger groups and other groups to care for Country/Place

  VC2M4ST01 | Mathematics | Mathematics Version 2.0 | Level 4 | Statistics

• VC2M5ST01

  acquire, validate and represent data for nominal and ordinal categorical and discrete numerical variables to address a question of interest or purpose using software including spreadsheets; discuss and report on data distributions in terms of highest frequency (mode) and shape, in the context of the data

  Elaborations

  • recognising that ordinal data is a form of categorical data even though the data being collected might be numbers, for example, a rating scale using numbers 1–5 to represent the categories people can choose from when asked, ‘What rating would you give this film out of 5?’
  • determining the mode for a set of data and discussing that there may be more than one mode
  • identifying the best methods of presenting data to illustrate the results of investigations and justifying the choice of representations
  • acquiring data through chance experiments, discussing and reporting on the distribution of outcomes and how this relates to equal and unequal outcomes
  • using digital systems to validate data; for example, recognising the difference between numerical, text and date formats in spreadsheets, and setting data types in a spreadsheet to make sure a date is input correctly
  • investigating data relating to the reconciliation process between Aboriginal and Torres Strait Islander Peoples and non-Indigenous Australians, posing questions, discussing and reporting on findings

  VC2M5ST01 | Mathematics | Mathematics Version 2.0 | Level 5 | Statistics

• VC2M8ST03

  compare variations in distributions and proportions obtained from random samples of the same size drawn from a population and recognise the effect of sample size on this variation

  Elaborations

  • comparing the proportion of students in favour of a proposal for a change in school uniform between different random samples of 50 students from the school population
  • using digital tools to simulate repeated sampling of the same population, such as heights or arm spans of students, recording and comparing means, median and range of data between samples
  • using relative frequencies from historical data to predict proportions and the likely number of outcomes in situations such as weather forecasting or the countries of origin of visitors to tourist attractions
  • investigating the effect that adding or removing data from a data set has on measures of central tendency and spread
  • investigating Aboriginal and/or Torres Strait Islander ranger groups and other groups’ use of sampling techniques to track biodiversity of species

  VC2M8ST03 | Mathematics | Mathematics Version 2.0 | Level 8 | Statistics

• VC2M9ST05

  plan and conduct statistical investigations involving the collection and analysis of different kinds of data; report findings and discuss the strength of evidence to support any conclusions

  Elaborations

  • planning and conducting an investigation using questions together with analysis of a secondary data set collected from online databases such as the Australian Bureau of Statistics
  • planning and conducting an investigation relating to consumer spending habits; and modelling market research on what teenagers are prepared to spend on technology compared to clothing, with consideration of sample techniques and potential sources of bias
  • investigating where would be the best location for a tropical fruit plantation, by conducting a statistical investigation comparing different variables such as the annual rainfall in various parts of Australia, Indonesia, New Guinea and Malaysia, land prices and associated farming costs
  • posing statistical questions; collecting, representing and interpreting data from different sources in relation to reconciliation between Aboriginal and Torres Strait Islander Peoples and non-Indigenous Australians; and considering the relationships between variables

  VC2M9ST05 | Mathematics | Mathematics Version 2.0 | Level 9 | Statistics

• VC2M2M01

  measure and compare objects based on length, capacity and mass using appropriate uniform informal units and smaller units for accuracy when necessary

  Elaborations

  • choosing suitable informal units to measure the length of a range of objects, and justifying their choice of a longer unit to measure things that are long (such as the width of a room) and a shorter unit to measure shorter things or when more accuracy is needed
  • comparing the capacity of several containers using sand and units such as a spoon or cup, to say which container will hold the most and how much more it will hold; recording the results; writing an explanation of their measurement process, including using smaller units to be more accurate; and justifying the result
  • using balance scales to compare the mass of several objects, selecting an appropriate informal unit; counting the number of informal units to determine which object is heavier and how much heavier; and explaining why the informal units chosen need to be the same mass
  • recognising that the same informal unit needs to be used when measuring (for example, demonstrating and discussing why using different shoe lengths to measure the same distance could result in the measures being different) and discussing why a smaller-sized informal unit may result in a larger number of units compared to a larger-sized informal unit
  • investigating Aboriginal and/or Torres Strait Islander Peoples’ use of body parts, such as hands, as uniform informal units of measurement used to measure and compare objects, for example, in the manufacturing of nets for a particular purpose
  • investigating and comparing measurable attributes that are interpreted by Aboriginal and/or Torres Strait Islander Peoples to understand animal behaviour, such as the length, width and depth of animal tracks

  VC2M2M01 | Mathematics | Mathematics Version 2.0 | Level 2 | Measurement

• VC2M10A15

  use mathematical modelling to solve applied problems involving inverse proportion, growth and decay, including in financial contexts to establish the compound interest formula as repeated applications of simple interest; formulate problems, choosing to apply linear, quadratic or exponential models...

  Elaborations

  • modelling problems involving inverse proportion in real-life contexts such as travel time decreasing with increased travel speed, the brightness of luminous objects decreasing with distance, or household expenditure and savings, and solving related equations
  • modelling situations and choosing between linear, quadratic and exponential models by representing relationships in a table of values and recognising that linear functions have constant first differences, quadratic functions have constant second differences and exponential functions have a constant ratio between consecutive values of the dependent variable
  • modelling situations involving exponential growth and decay, and contrasting this with linear growth or decay, for example, situations involving constant percentage change and constant ratio, and determining doubling time and half-life and approximate intervals for which the values of the model lie within a given range
  • modelling situations that involve working with authentic information, data and interest rates to calculate compound interest and solve related problems
  • modelling and investigating how exponential equations are used in carbon dating to estimate the age of Aboriginal and Torres Strait Islander artefacts or material culture
  • modelling situations involving the growth of native animal populations on Country/Place with varying reproductive behaviour, using exponential functions and critiquing their applicability to real-world situations

  VC2M10A15 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M3A01

  recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences

  Elaborations

  • partitioning numbers using materials, part-part-whole diagrams or bar models, and recording addition and subtraction facts for each representation, explaining how each fact is connected to the materials, diagrams or models (for example, 16 + 8 = 24, 24 − 8 = 16, 8 = 24 − 16)
  • using the inverse relationship between addition and subtraction to find unknown values with a calculator or by counting on; for example, representing the problem ‘Peter had some money and then spent $375. Now he has $158 left. How much did Peter have to start with?’ as □ − $375 = $158 and solving the problem using $375 + $158 = $533; or solving 27 + □ = 63 using subtraction, □ = 63 – 27, or by counting on 27, 37, 47, 57, 60, 63, so add 3 tens and 6 ones, so □ = 36
  • exploring Aboriginal and/or Torres Strait Islander Peoples’ stories and dances that show the connection between addition and subtraction, representing this as a number sentence and discussing how this conveys important information about balance in processes on Country/Place

  VC2M3A01 | Mathematics | Mathematics Version 2.0 | Level 3 | Algebra

• VC2M10ASP06

  design, test and refine solutions to spatial problems using algorithms and digital tools; communicate and justify solutions 

  Elaborations

  • designing and making scale models of three-dimensional objects using digital tools; for example, making components of a puzzle using a three-dimensional printer, and planning and designing the puzzle using principles of tessellations
  • applying a computational thinking approach to solving problems involving networks, for example, connectedness, coverage and weighted measures, such as taking different routes and choosing the most efficient route to take when travelling by car using virtual map software 
  • defining and decomposing spatial problems, creating and applying algorithms to generate solutions, and evaluating and communicating solutions in terms of the problem; for example, designing a floor plan for a department store that limits congestion at key areas such as check-outs, changing rooms and near popular sale items
  • designing, creating and testing algorithms using pseudocode or flow charts for producing self-similar patterns; and validating algorithms using a range of test cases to compare their output
  • exploring geospatial technologies used by Aboriginal and/or Torres Strait Islander communities, to consider spatial problems including position and transformation

  VC2M10ASP06 | Mathematics | Mathematics Version 2.0 | Level 10A | Space

• VC2MFN03

  quantify and compare collections to at least 20 using counting and explain or demonstrate reasoning

  Elaborations

  • establishing the language and process of counting, and understanding that each object must be counted only once, that the arrangement of objects does not affect how many there are and that the last number counted answers the question of ‘How many?’; for example, saying numbers in sequence while playing and performing actions
  • using counting to compare the size of 2 or more collections of like items to justify which collection contains more or fewer items
  • using counting and one-to-one correspondence to quantify the number of items required for a purpose; for example, when asked to collect enough scissors for each member of their group to have a pair, counting each member and using the total count to know how many to collect
  • discussing how different cultures may have alternative ways of representing the count; for example, discussing how some people of the Asia region use an abacus or Chinese hand gestures
  • using body-tallying that involves body parts and one-to-one correspondence from counting systems of Aboriginal and/or Torres Strait Islander Peoples to count to 20

  VC2MFN03 | Mathematics | Mathematics Version 2.0 | Foundation Level | Number

• VC2MFN05

  represent practical situations, including simple financial situations, involving addition, subtraction and quantification with physical and virtual materials and use counting or subitising strategies

  Elaborations

  • using role-play and materials to represent mathematical relationships in stories; for example, role-playing ‘Eight kangaroos were drinking at the river and 3 hopped away’, drawing a picture and using materials to represent the situation, discussing, and recording the result of the action with a numeral
  • role-playing or actively engaging in situations that involve quantifying or comparing collections of items or simple money transactions; for example, engaging with the question ‘Do we have enough scissors for our group so that each person has their own pair?’, or role-playing using $1 coins to pay for items in a shop where items are priced in whole dollars
  • representing situations expressed in Aboriginal and/or Torres Strait Islander stories, such as ‘Tiddalick, the greedy frog’, that describe additive situations and their connections to Country/Place
  • representing addition and subtraction situations found in leaf games involving sets of objects used to tell stories, such as games from the Warlpiri Peoples of Yuendumu in the Northern Territory

  VC2MFN05 | Mathematics | Mathematics Version 2.0 | Foundation Level | Number

• VC2MFN01

  name, represent and order numbers, including zero to at least 20, using physical and virtual materials and numerals

  Elaborations

  • responding to a request to collect a quantity of objects or reading a numeral and selecting the associated quantity of items from a collection to match the number required; for example, collecting 9 paintbrushes after hearing the word ‘nine’
  • recognising the order in the sequence of numbers to 20 and identifying the number that is ‘one less’ than a given number and the number that is ‘one more’; for example, playing instructive card games that involve reading and ordering number cards, or using counting songs, storybooks and rhymes to establish the forwards and backwards counting sequence of numbers in the context of active counting activities
  • understanding and using terms to indicate ordinal position in a sequence; for example, filling in the missing term in ‘first’, ‘second’, ‘third’, … ‘fifth’ …, or creating a number track using cards with the numerals zero to 20 and describing positions using terms such as ‘first’, ‘last’, ‘before’, ‘after’ and ‘between’
  • recognising, writing and reading numerals written on familiar objects; for example, recognising and reading numerals in images, text or illustrations in storybooks, or writing a numeral on a container as a label to show how many objects it contains
  • connecting quantities to number names and numerals when reading and reciting stories and playing counting games or determining and reasoning about the size of sets of objects within Aboriginal and/or Torres Strait Islander Peoples’ instructive games, for example, Segur etug from Mer Island in the Torres Strait region

  VC2MFN01 | Mathematics | Mathematics Version 2.0 | Foundation Level | Number

• VC2MFST01

  collect, sort and compare data represented by objects and images in response to given investigative questions that have only 2 outcomes and relate to familiar situations

  Elaborations

  • using data displays to answer simple questions such as ‘How many students answered “yes” to having pets?’
  • collecting and deciding how to organise data to answer yes/no questions; for example, in relation to the question ‘Do more people in our class today have shoes with laces than without?’, explaining that lining up and matching shoes with and without laces one-to-one will answer the question
  • collecting data through everyday activities or events and sorting the collected data; for example, sorting toys into categories such as ‘toys that move’ and ‘toys that don’t move’
  • creating classroom charts and rosters using stickers to represent data; and comparing and interpreting the representations
  • investigating statistical contexts after reading a story; for example, after reading The Waterhole by Graeme Base, asking and responding to questions like ‘What different animals did you see?’, ‘How many different types of animals were there?’ or ‘Were there more tigers or kangaroos?’
  • exploring what and how information from the environment is collected and used by Aboriginal and/or Torres Strait Islander Peoples to predict weather events

  VC2MFST01 | Mathematics | Mathematics Version 2.0 | Foundation Level | Statistics

• VC2M7M03

  describe the relationship between π and the circumference, radius and diameter of a circle

  Elaborations

  • recognising the features of circles and their relationships to one another; for example, labelling the parts of a circle including centre, radius, diameter and circumference and using one of radius, diameter or circumference to determine the measure of the other 2; and understanding that the diameter of a circle is twice the radius, or that the radius is the circumference divided by 2π
  • comparing the circumference of circles in relation to their radius and diameter with materials and measuring, to establish measurement formulas; for example, using a compass to draw several circles, then using string to approximate the circumference, comparing the length of string to the diameter of the circle
  • investigating π as the constant in the proportional relationship between the circumference of a circle and its diameter, and historical approximations from different civilisations, including Egypt, Babylon, Greece, India and China
  • investigating the applications and significance of circles in everyday life of Aboriginal and Torres Strait Islander Peoples, such as in basketry, symbols and architecture, recognising the relationships between the centre, radius, diameter and circumference

  VC2M7M03 | Mathematics | Mathematics Version 2.0 | Level 7 | Measurement

• VC2M4M01

  use scaled and digital instruments to interpret unmarked and partial units to measure and compare lengths, masses, capacities, durations and temperatures, using appropriate units

  Elaborations

  • reading the mass of objects measured with digital and analog kitchen scales and explaining what unit of mass the lines on the analog scales refer to
  • deciding on which attribute, unit and measuring instrument to use to compare the length and mass of various things, such as the distance travelled by an object in a science investigation; and explaining the use of units such as grams or millimetres to give accurate measures when needed
  • using scaled instruments such as tape measures, measuring jugs, kitchen scales and thermometers to record measures using whole units (for example, 560 millimetres) or whole and part units (for example, 5.25 metres, 1.75 litres, 2.5 kilograms, 28.5° Celsius)
  • reading and interpreting the scale of an analog clock without marked minutes to estimate the time to the nearest minute and to determine the duration of time between events
  • using the timer or alarm function of a clock to alert when a specified duration has elapsed from a given starting time, for example, for the different activities of an exercise routine
  • making a scaled measuring instrument such as a tape measure, ruler, sand timer, sundial or measuring cup using scaled instruments and direct comparisons
  • exploring the different types of scaled instruments used by Aboriginal and/or Torres Strait Islander ranger groups and other groups to make decisions about caring for Country/Place, and modelling these in local contexts

  VC2M4M01 | Mathematics | Mathematics Version 2.0 | Level 4 | Measurement

• VC2M5M02

  solve practical problems involving the perimeter and area of regular and irregular shapes using appropriate metric units

  Elaborations

  • investigating problem situations involving perimeter, for example, ‘How many metres of fencing are required around a paddock, or around a festival event?’
  • using efficient ways to calculate the perimeters of rectangles, such as adding the length and width together and doubling the result
  • solving measurement problems such as ‘How much carpet would be needed to cover the entire floor of the classroom?’, using square metre templates to directly measure the floor space
  • creating a model of a permaculture garden, dividing the area up to provide the most efficient use of space for gardens and walkways, labelling the measure of each area, and calculating the amount of resources needed, for example, compost to cover the vegetable garden
  • using a physical geoboard or a virtual geoboard app to recognise the relationship between area and perimeter and solve problems; for example, investigating what is the largest and what is the smallest area that has the same perimeter
  • exploring the designs of fishing nets and dwellings of Aboriginal and Torres Strait Islander Peoples, investigating the perimeter, area and purpose of the shapes within the designs

  VC2M5M02 | Mathematics | Mathematics Version 2.0 | Level 5 | Measurement

• VC2M2N06

  use mathematical modelling to solve practical problems involving additive and multiplicative situations, including money transactions; represent situations and choose calculation strategies; interpret and communicate solutions in terms of the context

  Elaborations

  • modelling practical problems by interpreting an everyday additive or multiplicative situation; for example, making a number of purchases at a store and deciding whether to use addition, subtraction, multiplication or division to solve the problem and justifying the choice of operation, such as ‘I used subtraction to solve this problem as I knew the total and one of the parts, so I needed to subtract to find the missing part’
  • modelling and solving simple money problems involving whole dollar amounts with addition, subtraction, multiplication or division, for example, ‘If each member of our class contributes $5, how much money will we have in total?’
  • modelling and solving practical problems such as deciding how many people should be in each team for a game or sports event, how many teams for a given game can be filled from a class, or how to share out some food or distribute money in whole dollar amounts, including deciding what to do if there is a remainder
  • modelling and solving the problem ‘How many days are there left in this year?’ by using a calendar
  • modelling problems involving equal grouping and sharing in Aboriginal and/or Torres Strait Islander children’s instructive games; for example, in Yangamini from the Tiwi Peoples of Bathurst Island, representing relationships with a number sentence and interpreting and communicating solutions in terms of the context

  VC2M2N06 | Mathematics | Mathematics Version 2.0 | Level 2 | Number

• VC2M3N02

  recognise, represent and order natural numbers using naming and writing conventions for numerals beyond 10 000

  Elaborations

  • moving materials from one place to another on a place value model to show renaming of numbers (for example, 1574 can be shown as one thousand, 5 hundreds, 7 tens and 4 ones, or as 15 hundreds, 7 tens and 4 ones)
  • using the repeating pattern of place value names and spaces within sets of 3 digits to name and write larger numbers: ones, tens, hundreds, ones of thousands, tens of thousands, hundreds of thousands, ones of millions, tens of millions; for example, writing four hundred and twenty-five thousand as 425 000
  • predicting and naming the number that is one more than 99, 109, 199, 1009, 1099, 1999, 10 009 … 99 999 and discussing what will change when one, one ten and one hundred is added to each
  • comparing the Hindu-Arabic numeral system to other numeral systems; for example, investigating the Japanese numeral system, 一、十、百、千、万
  • comparing, reading and writing the numbers involved in more than 60 000 years of Aboriginal and Torres Strait Islander Peoples’ presence on the Australian continent through timescales relating to pre-colonisation and post-colonisation

  VC2M3N02 | Mathematics | Mathematics Version 2.0 | Level 3 | Number

• VC2M7N10

  use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts such as ‘best buys’; formulate problems, choosing representations and efficient calculation strategies, designing algorithms and using digital tools as appropriate; interpret...

  Elaborations

  • modelling additive situations involving positive and negative quantities; for example, a lift travelling up and down floors in a high-rise apartment where the ground floor is interpreted as zero, or in geography when determining altitude above and below sea level
  • modelling contexts involving proportion, such as the proportion of students attending the school disco, proportion of the bottle cost to the recycling refund, proportion of the school site that is green space, 55% of Year 7 students attended the end of term function or 23% of the school population voted ‘yes’ to a change of school uniform; and interpreting and communicating answers in terms of the context of the situation
  • modelling financial problems involving profit and loss, credits and debits, gains and losses; for example, holding a fundraising sausage sizzle and determining whether the event made a percentage profit or loss
  • finding the sum of a set of consecutive numbers using a loop structure
  • constructing geometric patterns such as a honeycomb, using dynamic geometry functionality
  • using mathematical modelling to investigate the proportion of land mass/area of Aboriginal Peoples’ traditional grain belt compared with Australia’s current grain belt

  VC2M7N10 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M8P02

  determine all possible outcome combinations for 2 events, using two-way tables, tree diagrams and Venn diagrams, and use these to determine probabilities of specific events in practical situations

  Elaborations

  • describing events using language of ‘at least’, exclusive ‘or’ (A or B but not both), inclusive ‘or’ (A or B or both) and ‘and’
  • using the relation Pr(A and B) + Pr(A and not B) + Pr(not A and B) + Pr(not A and not B) = 1 to calculate probabilities, including the special case of mutually exclusive events where Pr(A and B) = 0
  • using Venn diagrams or two-way tables to demonstrate the difference between events that are mutually exclusive, such as whether a coin toss will land on a head or a tail, and those that are not mutually exclusive, such as people who have blonde hair and people who have blue eyes
  • exploring Aboriginal and/or Torres Strait Islander children’s instructive games, for example, Battendi from the Ngarrindjeri Peoples of Lake Murray and Lake Albert in southern Australia, applying possible combinations and relationships and calculating probabilities using two-way tables and Venn diagrams

  VC2M8P02 | Mathematics | Mathematics Version 2.0 | Level 8 | Probability