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• 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

• VC2M6N05

  solve problems involving addition and subtraction of fractions using knowledge of equivalent fractions

  Elaborations

  • representing addition and subtraction of fractions, using an understanding of equivalent fractions and methods such as jumps on a number line, or diagrams of fractions as parts of shapes
  • determining the lowest common denominator using an understanding of prime and composite numbers to find equivalent representation of fractions when solving addition and subtraction problems
  • calculating the addition or subtraction of fractions in the context of real-world problems (for example, using part cups or spoons in a recipe), using the understanding of equivalent fractions
  • understanding the processes for adding and subtracting fractions with related denominators and fractions as an operator, in preparation for calculating with all fractions; for example, using fraction overlays and number lines to give meaning to adding and subtracting fractions with related and unrelated denominators

  VC2M6N05 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• VC2M4N01

  recognise and extend the application of place value to tenths and hundredths and use the conventions of decimal notation to name and represent decimals

  Elaborations

  • using a bar to represent the whole, dividing it into 10 equal pieces with each piece representing 0.1 or one-tenth of the whole length and understanding that 2 pieces are 0.2 or two-tenths of the whole
  • using materials to show the multiplicative relationship between the whole, tenths and hundredths; for example, using a bundle of 10 straws to represent the whole, one straw as the tenth, and cutting the tenth into 10 parts to show the hundredths; or using deci-pipes to represent tenths
  • recognising that one is the same as ten-tenths and one-tenth is the same as ten-hundredths and using this relationship to rename decimals; for example, renaming 0.25 as two-tenths and five-hundredths or twenty-five-hundredths
  • making models of measurement attributes to show the relationship between the base unit and parts of the unit, for example, 1.5 metres is one metre and five-tenths of the next metre; 1.75 units is one unit and seventy-five-hundredths of the next unit
  • counting large quantities of mixed notes and coins, writing the total using dollars and cents, and recognising the cents as parts of the next dollar
  • comparing the way money and measures are read and said, and explaining how they are the same and different; for example, explaining that $2.75 is said ‘two dollars seventy-five’ and 2.75 metres is said ‘two point seven five metres’, and recognising that the 7 means seven-tenths and the 5 means five-hundredths in both

  VC2M4N01 | Mathematics | Mathematics Version 2.0 | Level 4 | 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

• VC2M3N08

  use mathematical modelling to solve practical problems involving additive and multiplicative situations, including financial contexts; formulate problems using number sentences and choose calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms...

  Elaborations

  • modelling practical additive situations, choosing whether to use an addition, subtraction or both when representing the problem as a number sentence, and explaining how each number in their number sentence is connected to the situation
  • modelling additive problems using a bar model to represent the problem; for example, modelling the problem ‘I had 75 tomatoes and then picked some more. Now I have 138. How many did I pick?’
  • modelling practical multiplicative situations using materials or a diagram to represent the problem; for example, if 4 tomato plants each have 6 tomatoes, deciding whether to use an addition or multiplication number sentence, explaining how each number in their number sentence is connected to the situation
  • modelling and solving practical division problems involving unknown numbers of groups or finding how much is in each group by representing the problem with both division and multiplication number sentences, and explaining how the 2 number sentences are connected to the problem
  • modelling the problem of deciding how to share an amount equally (for example, 48 horses into 2, 4, 6 or 8 paddocks), representing the shares with a division and a multiplication number sentence, and counting the number in each share to check the solutions

  VC2M3N08 | Mathematics | Mathematics Version 2.0 | Level 3 | Number

• 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

• VC2M5N10

  follow a mathematical algorithm involving branching and repetition (iteration); create and use algorithms involving a sequence of steps and decisions and digital tools to experiment with factors, multiples and divisibility; identify, interpret and describe emerging patterns

  Elaborations

  • simulating a simple random walk
  • manipulating sets of numbers using a given rule, for example, if a number is even, halve it; or if a number is odd, subtract 1 then halve it
  • creating algorithms that use multiplication and division facts to determine if a number is a multiple or factor of another number; for example, using a flow chart that determines whether numbers are factors or multiples of other numbers using branching, such as yes/no decisions
  • identifying lowest common multiples and highest common factors of pairs or triples of natural numbers; for example, the lowest common multiple of {6, 9} is 18, and the highest common factor is 3, and the lowest common multiple of {3, 4, 5} is 60 and the highest common factor is 1
  • using the ‘fill down’ function of a spreadsheet and a multiplication formula to generate a sequence of numbers that represent the multiples of any number you enter into the cell, and describing and explaining the emerging patterns

  VC2M5N10 | Mathematics | Mathematics Version 2.0 | Level 5 | Number

• VC2M3N07

  recognise the relationships between dollars and cents and represent money values in different ways

  Elaborations

  • investigating the relationship between dollars and cents, using physical or virtual materials to make different combinations of the same amount of money
  • representing money amounts in different ways using knowledge of part-part-whole relationships; for example, knowing that $1 is equal to 100 cents, representing $1.85 as $1 + 50c + 20c + 10c + 5c or 50c + 50c + 50c + 10c + 10c + 10c + 5c; or when calculating change from buying an item for $1.30 from $2, starting from $1.30 and adding 20c and 50c, which gives $2

  VC2M3N07 | Mathematics | Mathematics Version 2.0 | Level 3 | Number

• VC2M6N01

  recognise situations, including financial contexts, that use integers; locate and represent integers on a number line and as coordinates on the Cartesian plane

  Elaborations

  • extending the number line in the negative direction to locate and represent integers, recognising the difference in location between (−2) and (+2) and their relationship to zero as −2 < 0 < 2
  • using integers to represent quantities in financial contexts, including the concept of profit and loss for a planned event
  • using horizontal and vertical number lines to represent and find solutions to everyday problems involving locating and ordering integers around zero (for example, elevators, above and below sea level) and distinguishing a location by referencing the 4 quadrants of the Cartesian plane
  • recognising that the sign (positive or negative) indicates a direction in relation to zero – for example, 30 metres left of the admin block is (−30) and 20 metres right of the admin block is (+20) – and programming robots to move along a number line that is either horizontal or vertical but not both at the same time
  • representing the temperatures of the different planets in the solar system, using a diagram of a thermometer that models a vertical number line

  VC2M6N01 | Mathematics | Mathematics Version 2.0 | Level 6 | 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

• VC2M5N05

  solve problems involving addition and subtraction of fractions with the same or related denominators, using different strategies

  Elaborations

  • using different ways to add and subtract fractional amounts by subdividing different models of measurement attributes; for example, adding half an hour and three-quarters of an hour using a clock face, adding a 34 cup of flour and a 14 cup of flour, subtracting 34 of a metre from 2 14 metres
  • representing and solving addition and subtraction problems involving fractions by using jumps on a number line, or bar models, or making diagrams of fractions as parts of shapes
  • using materials, diagrams, number lines or arrays to show and explain that fraction number sentences can be rewritten in equivalent forms without changing the quantity, for example, 12+14 is the same as 24+14 

  VC2M5N05 | Mathematics | Mathematics Version 2.0 | Level 5 | Number

• 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

• 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

• VC2M6N09

  use mathematical modelling to solve practical problems involving rational numbers and percentages, including in financial contexts; formulate the problems, choosing operations and using efficient mental and written calculation strategies, and using digital tools where appropriate; interpret and...

  Elaborations

  • modelling practical situations involving percentages using efficient calculation strategies to find solutions, such as mental calculations, spreadsheets, calculators or a variety of informal jottings, and interpreting the results in terms of the situation, for example, purchasing items during a sale
  • modelling situations involving earning money and budgeting, asking questions such as ‘Can I afford it?’, ‘Do I need it?’ and ‘How much do I need to save for it?’ and developing a savings plan or budget for an upcoming event or personal purchase
  • modelling and solving the problem of creating a budget for a class excursion or family holiday, using the internet to research costs and expenses, and representing the budget in a spreadsheet, creating and using formulas to calculate totals

  VC2M6N09 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• VC2M5N09

  use mathematical modelling to solve practical problems involving additive and multiplicative situations, including simple financial planning contexts; formulate the problems, choosing operations and efficient mental and written calculation strategies, and using digital tools where appropriate;...

  Elaborations

  • modelling an everyday situation and determining which operations can be used to solve it using materials, diagrams, arrays and/or bar models to represent the problem; formulating the situation as a number sentence; and justifying their choice of operations in relation to the situation
  • modelling a series of contextual problems, deciding whether an exact answer or an approximate calculation is appropriate, and explaining their reasoning in relation to the context and the numbers involved
  • modelling financial situations such as creating financial plans; for example, creating a budget for a class fundraising event, using a spreadsheet to tabulate data and perform calculations
  • investigating how mathematical models involving combinations of operations can be used to represent songs, stories and/or dances of Aboriginal and Torres Strait Islander Peoples

  VC2M5N09 | Mathematics | Mathematics Version 2.0 | Level 5 | Number

• VC2M6N04

  apply knowledge of place value to add and subtract decimals, using digital tools where appropriate; use estimation and rounding to check the reasonableness of answers

  Elaborations

  • applying estimation strategies to addition and subtraction of decimals to at least thousandths before calculating answers or when a situation requires just an estimation
  • applying whole-number strategies; for example, using basic facts, place value, partitioning and the inverse relationship between addition and subtraction, and properties of operations to develop meaningful mental strategies for addition and subtraction of decimal numbers to at least hundredths
  • working additively with linear measurements expressed as decimals up to 2 and 3 decimal places; for example, calculating how far off the world record the athletes were at the last Olympic Games in the women’s long jump or shot-put and comparing school records to the Olympic records
  • deciding to use a calculator as a calculation strategy for solving additive problems involving decimals that vary in their number of decimal places beyond hundredths; for example, 1.0 − 0.0035 or 2.345 + 1.4999

  VC2M6N04 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• VC2M7N06

  use the 4 operations with positive rational numbers, including fractions and decimals, to solve problems using efficient mental and written calculation strategies

  Elaborations

  • solving addition and subtraction problems involving fractions and decimals; for example, using rectangular arrays with dimensions equal to the denominators, algebra tiles, digital tools or informal jottings
  • choosing an appropriate numerical representation for a problem so that efficient computations can be made, such as 12.5%, 18, 0.125 or 1251000
  • developing efficient strategies with appropriate use of the commutative and associative properties, place value, patterning, and multiplication facts to solve multiplication and division problems involving fractions and decimals; for example, using the commutative property to calculate 23 of 12 , giving 12 of 23=13
  • solving multiplicative problems involving fractions and decimals using fraction walls, rectangular arrays, algebra tiles, calculators or informal jottings
  • developing efficient strategies with appropriate use of the commutative and associative properties, regrouping or partitioning to solve additive problems involving fractions and decimals
  • carrying out calculations to solve problems using the representation that makes computations efficient, such as 12.5% of 96 is more efficiently calculated as 18 of 96, including contexts such as comparing land use by calculating the total local municipal area set aside for parkland or manufacturing and retail, the amount of protein in daily food intake across several days, or increases or decreases in energy accounts each account cycle

  VC2M7N06 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M4N05

  solve problems involving multiplying or dividing natural numbers by multiples and powers of 10 without a calculator, using the multiplicative relationship between the place value of digits

  Elaborations

  • using physical or virtual materials to demonstrate the multiplicative relationship between the places
  • using materials such as place value charts, numeral expanders or sliders to recognise and explain why multiplying by 10 moves the digits one place to the left and dividing by 10 moves digits one place to the right
  • using a calculator or other digital tools to recognise and develop an understanding of the effect of multiplying or dividing numbers by tens, hundreds and thousands, recording sequences in a place value chart, in a table or spreadsheet, generalising the patterns noticed and applying them to solve multiplicative problems without a calculator

  VC2M4N05 | Mathematics | Mathematics Version 2.0 | Level 4 | Number

• VC2M3N05

  multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies

  Elaborations

  • applying knowledge of numbers and the properties of operations using a variety of ways to represent multiplication or division number sentences; for example, using a Think Board to show different ways of visualising 8 × 4, such as an array, a diagram and a worded problem
  • using part-part-whole and comparative models to visually represent multiplicative relationships and choosing whether to use multiplication or division to solve problems
  • matching or creating a problem scenario or story that can be represented by a given number sentence involving multiplication and division; for example, using given number sentences to create worded problems for others to solve
  • formulating connected multiplication and division expressions by representing situations from Aboriginal and/or Torres Strait Islander Peoples’ cultural stories and dances about how they care for Country/Place, such as turtle egg gathering, using number sentences

  VC2M3N05 | Mathematics | Mathematics Version 2.0 | Level 3 | Number

• VC2M4N09

  use mathematical modelling to solve practical problems that involve additive and multiplicative situations, including financial contexts; formulate the problems using number sentences and choose efficient calculation strategies, using digital tools where appropriate; interpret and communicate...

  Elaborations

  • modelling and solving a range of practical additive problems using materials, part-part-whole diagrams and/or a bar model, and writing addition and/or subtraction number sentences, based on whether a part or the whole is missing; and explaining how each number in their number sentence is connected to the situation
  • modelling practical problems with division, interpreting and representing the situation using a diagram or array to represent what is unknown (the number of groups, or the number per group); and writing a division number sentence to represent the situation and choosing an efficient calculation strategy
  • modelling practical problems involving money (such as a budget for a large event) that require either addition, subtraction, multiplication or division and justifying the choice of operation in relation to the situation
  • modelling and solving multiplication problems involving money, such as buying 5 toy scooters for $96 each, using efficient mental strategies and written jottings to keep track if needed; for example, rounding $96 up to $100 and subtracting 5 × $4 = $20, so 5 × $96 is the same as 5 × $100 less $20, giving the answer $500 − $20 = $480
  • modelling situations by formulating comparison problems using number sentences, comparison models and arrays; for example, ‘Ariana read 16 books for the “readathon”; Maryam read 4 times as many books. How many books did Maryam read?’ using the expression 4 × 16 and using place value partitioning, basic facts and an array, thinking 4 × 10 = 40 and 4 × 6 = 24, so 4 × 16 can be written as 40 + 24 = 64

  VC2M4N09 | Mathematics | Mathematics Version 2.0 | Level 4 | Number