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• 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

• VC2M3N04

  add and subtract two- and three-digit numbers using place value to partition, rearrange and regroup numbers to assist in calculations without a calculator

  Elaborations

  • using partitioning and part-part-whole models and the inverse relationship between addition and subtraction to solve addition or subtraction problems, making informal written ‘jottings’ to keep track of the numbers if necessary
  • using physical or virtual grouped materials or diagrams to make proportional models of numbers to assist in calculations, for example, to calculate 214 + 325, representing 214 as 2 groups of 100, one group of 10 and 4 ones and 325 as 3 groups of 100, 2 groups of 10 and 5 ones, resulting in 5 groups of 100, 3 groups of 10 and 9 ones, which is 539
  • choosing between standard and non-standard place value partitions to assist with calculations, for example, to solve 485 + 365, thinking of 365 as 350 + 15, then adding the parts, 485 + 15 = 500, 500 + 350 = 850
  • solving subtraction problems efficiently by adding or subtracting a constant amount to both numbers to create an easier calculation; for example, 534 − 395, adding 5 to both numbers to make 539 − 400 = 139
  • justifying choices about partitioning and regrouping numbers in terms of their usefulness for particular calculations when solving problems
  • applying knowledge of place value to assist in calculations when solving problems involving larger numbers; for example, calculating the total crowd numbers for an agricultural show that lasts a week

  VC2M3N04 | Mathematics | Mathematics Version 2.0 | Level 3 | Number

• VC2M7A04

  investigate, interpret and describe relationships between variables represented in graphs of functions developed from authentic data

  Elaborations

  • using graphs to analyse a building’s electricity or gas usage over a period of time, the value of shares on a stock market, or the temperature during a day, interpreting and discussing the relationships they represent
  • using travel graphs to compare the distance travelled to and from school, interpreting and discussing features of travel graphs such as the slope of lines and the meaning of horizontal line segments
  • telling the story behind what is being represented in graphs of functions, for example, graphs representing pouring rates or distance versus time
  • using graphs of evaporation rates to explore and discuss Aboriginal and Torres Strait Islander Peoples’ methods of water resource management

  VC2M7A04 | Mathematics | Mathematics Version 2.0 | Level 7 | Algebra

• VC2M1M01

  compare directly and indirectly and order objects and events using attributes of length, mass, capacity and duration, communicating reasoning

  Elaborations

  • using a piece of string to indirectly compare the length of several objects, deciding which will fit within a space, and using comparative language to describe the order (shortest, short, longer, longest)
  • ordering the mass of 3 or more objects, such as rocks, using hefting and balance scales, and using comparative language to explain the order (lightest, light, heavier, heaviest) and how they decided on the order
  • pouring sand, rice or water from one container to another to compare and order the capacity of 3 or more containers, and describing the order of the results in terms of which holds the most/least and those in between
  • creating sand timers from everyday items or recycled materials and comparing them to order the duration of time required for the sand to run through
  • investigating situations where Aboriginal and/or Torres Strait Islander Peoples estimate, compare and communicate measurements, for example, situations involving the duration of seasons, understanding animal behaviour using the length of animal tracks, or investigating capacity through Aboriginal and/or Torres Strait Islander water management techniques, such as traditional water-carrying vessels and rock holes

  VC2M1M01 | Mathematics | Mathematics Version 2.0 | Level 1 | Measurement

• Mathematics Version 2.0: Level 2 achievement standards

  By the end of Level 2, students order and represent numbers to at least 1000; apply knowledge of place value to partition, rearrange and rename two- and three-digit numbers in terms of their parts; and regroup partitioned numbers to assist in calculations. They use mathematical modelling...

  Level description | Mathematics | Mathematics Version 2.0 | Level 2

• Mathematics Version 2.0: Level 3 achievement standards

  By the end of Level 3, students order and represent natural numbers beyond 10 000, classify numbers as either odd or even, and use the properties of odd and even numbers. They partition, rearrange and regroup two- and three-digit numbers in different ways to assist in calculations. Students...

  Level description | Mathematics | Mathematics Version 2.0 | Level 3

• VC2M10M02

  interpret and use logarithmic scales in applied contexts involving small and large quantities and change 

  Elaborations

  • understanding that the logarithmic scale is calibrated in terms of order of magnitude, for example, doubling or powers of 10
  • identifying and interpreting data representations (charts and graphs) that use logarithmic scales (for example, graphs representing percentage change, a wide range of values or exponential growth) and discussing when it is appropriate to use this type of scale and when it is not appropriate
  • investigating and interpreting logarithmic scales used in real-world contexts (for example, Richter, decibel and sensitivity scales or growth in investments, timescales and the spread of microorganisms and disease) and describing reasons for choosing to use a logarithmic scale rather than a linear scale
  • investigating dating methods of geological sites to provide evidence of Aboriginal and Torres Strait Islander Peoples’ presence in Australia, including the Madjedbebe dig in the Northern Territory, that use logarithmic scales, scientific notation and measurement accuracy in the dating

  VC2M10M02 | Mathematics | Mathematics Version 2.0 | Level 10 | Measurement

• Mathematics Version 2.0: Level 7 achievement standards

  By the end of Level 7, students represent natural numbers in expanded form and as products of prime factors, using exponent notation. They solve problems involving squares of numbers and square roots of perfect square numbers. Students solve problems involving addition and subtraction...

  Level description | Mathematics | Mathematics Version 2.0 | Level 7

• Mathematics Version 2.0: Level 9 description

  In Level 9, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to the learning and doing of mathematics that develop their understanding of and fluency with concepts, procedures and processes by making connections, reasoning...

  Level description | Mathematics | Mathematics Version 2.0

• Mathematics Version 2.0: Level 7 description

  In Level 7, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to the learning and doing of mathematics that develop their understanding of and fluency with concepts, procedures and processes by making connections...

  Level description | Mathematics | Mathematics Version 2.0

• 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

• VC2M3N09

  follow and create algorithms involving a sequence of steps and decisions to investigate numbers; describe any emerging patterns

  Elaborations

  • following or creating an algorithm to generate number patterns formed by doubling and halving using technology to assist, where appropriate, and identifying and describing emerging patterns
  • following or creating an algorithm that determines whether a given number is a multiple of 2, 5 or 10, identifying and discussing emerging patterns
  • creating an algorithm as a set of instructions that a classmate can follow to generate multiples of 3 using the rule ‘To multiply by 3 you double the number and add on one more of the number’ (for example, for 3 threes, you double 3 and add on 3 to get 9; for 3 fours you double 4 and add one more 4 to get 12 …)
  • creating a sorting algorithm that will sort a collection of 5-cent and 10-cent coins and providing the total value of the collection by applying knowledge of multiples of 5 and 10

  VC2M3N09 | Mathematics | Mathematics Version 2.0 | Level 3 | Number

• 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

• VC2M5N01

  interpret, compare and order numbers with more than 2 decimal places, including numbers greater than one, using place value understanding; represent these on a number line

  Elaborations

  • making models of decimals including tenths, hundredths and thousandths by subdividing materials or grids, and explaining the multiplicative relationship between consecutive places; for example, explaining that thousandths are 10 times smaller than hundredths, or writing numbers into a place value chart to compare and order them
  • renaming decimals to assist with mental computation; for example, when asked to solve 0.6 ÷ 10 they rename 6 tenths as 60 hundredths and say, ‘If I divide 60 hundredths by 10, I get 6 hundredths’ and write 0.6 ÷ 10 = 0.06
  • using a number line or number track to represent and locate decimals with varying numbers of decimal places and numbers greater than one and justifying the placement; for example, 2.335 is halfway between 2.33 and 2.34, that is, 2.33 < 2.335 < 2.34, and 5.283 is between 5.28 and 5.29 but closer to 5.28
  • interpreting and comparing the digits in decimal measures, for example, the length or mass of animals or plants, such as a baby echidna weighing 1.78 kilograms and a platypus weighing 1.708 kilograms
  • interpreting plans or diagrams showing length measures as decimals, placing the numbers into a decimal place value chart to connect the digits to their value

  VC2M5N01 | Mathematics | Mathematics Version 2.0 | Level 5 | Number

• 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

• VC2M2N04

  add and subtract one- and two-digit numbers, represent problems using number sentences and solve using part-part-whole reasoning and a variety of calculation strategies

  Elaborations

  • using the associative property of addition to assist with mental calculation by partitioning, rearranging and regrouping numbers using number knowledge, near doubles and bridging-to-10 strategies; for example, calculating 7 + 8 using 7 + (7 + 1) = (7 + 7) + 1, the associative property and near doubles; or calculating 7 + 8 using the associative property and bridging to 10: 7 + (3 + 5) = (7 + 3) + 5
  • using strategies such as doubles, near doubles, part-part-whole knowledge to 10, bridging tens and partitioning to mentally solve problems involving two-digit numbers; for example, calculating 56 + 37 by thinking 5 tens and 3 tens is 8 tens, 6 + 7 = 6 + 4 + 3 is one 10 and 3, and so the result is 9 tens and 3, or 93
  • representing addition and subtraction problems using a bar model and writing a number sentence, explaining how each number in the sentence is connected to the situation
  • using mental strategies and informal written jottings to help keep track of the numbers when solving addition and subtraction problems involving two-digit numbers and recognising that zero added to a number leaves the number unchanged; for example, in calculating 34 + 20 = 54, 3 tens add 2 tens is 5 tens, which is 50, and 4 ones add zero ones is 4 ones, which is 4, so the result is 50 + 4 = 54
  • using a physical or mental number line or hundreds chart to solve addition or subtraction problems by moving along or up and down in tens and ones; for example, solving the problem ‘I was given a $100 gift card for my birthday and spent $38 on a pair of shoes and $15 on a T-shirt. How much money do I have left on the card?’
  • using Aboriginal and Torres Strait Islander Peoples’ stories and dances to understand the balance and connection between addition and subtraction, representing relationships as number sentences

  VC2M2N04 | Mathematics | Mathematics Version 2.0 | Level 2 | Number

• VC2M5N03

  compare and order common unit fractions with the same and related denominators, including mixed numerals, applying knowledge of factors and multiples; represent these fractions on a number line

  Elaborations

  • using pattern blocks to represent equivalent fractions; selecting one block or a combination of blocks to represent one whole, and making a design with shapes; and recording the fractions to justify the total
  • creating a fraction wall from paper tape to model and compare a range of different fractions with related denominators, and using the model to play fraction wall games
  • connecting a fraction wall model and a number line model of fractions to say how they are the same and how they are different; for example, explaining 14 on a fraction wall represents the area of one-quarter of the whole, while on the number line 14 is identified as a point that is one-quarter of the distance between zero and one
  • using an understanding of factors and multiples as well as equivalence to recognise efficient methods for the location of fractions with related denominators on parallel number lines; for example, explaining on parallel number lines that 210 is located at the same position on a parallel number line as 15 because 15 is equivalent to 210
  • converting between mixed numerals and improper fractions to assist with locating them on a number line

  VC2M5N03 | Mathematics | Mathematics Version 2.0 | Level 5 | Number