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• VC2M10A13

  solve simple quadratic equations using a range of strategies, including null factor law

  Elaborations

  • using techniques to solve quadratic equations, including grouping like terms, completing the square, the quadratic formula and null factor law, and choosing 2 integers with the required product and sum
  • using digital tools to explore the conditions for solutions to exist
  • using digital tools to explore both graphically and algebraically the link between the value of the discriminant and the number of real solutions to a quadratic equation

  VC2M10A13 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• 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

• VC2M7N04

  round decimals to a given accuracy appropriate to the context and use appropriate rounding and estimation to check the reasonableness of computations

  Elaborations

  • identifying the interval between a pair of consecutive integers that includes a given rational number
  • choosing and applying conventions for rounding correct to a specified number of decimal places based upon the context
  • checking that the accuracy of rounding is suitable for context and purpose; for example, for the amount of paint required or the cost estimate for renovating a house, purchasing 2 litres of paint to paint the bedroom even though 1.89 litres is the exact answer or estimating a renovation budget to the nearest $100

  VC2M7N04 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VCMNA133

  Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation

  Elaborations

  • recognising that certain single-digit number combinations always result in the same answer for addition and subtraction, and using this knowledge for addition and subtraction of larger numbers
  • extending strategies for addition and subtraction such as 14 + 8 + 6 = 14 + 6 + 8 = 28 and 54 – 28 = 2 + 20 + 4
  • combining knowledge of addition and subtraction facts and partitioning to aid computation. For example, 57 + 19 = 57 + 20 – 1

  VCMNA133 | Mathematics | Level 3 | Number and Algebra | Number and place value

• VC2M8P03

  conduct repeated chance experiments and simulations, using digital tools to determine probabilities for compound events, and describe results

  Elaborations

  • using digital tools to conduct probability simulations involving compound events
  • using a random number generator and digital tools to simulate rolling 2 dice and calculating the difference between them, investigating what difference is likely to occur more often
  • using online simulation software to conduct probability simulations to determine in the long run if events are complementary

  VC2M8P03 | Mathematics | Mathematics Version 2.0 | Level 8 | Probability

• VC2M6P01

  describe probabilities using fractions, decimals and percentages; recognise that probabilities lie on numerical scales of 0–‍1 or 0%–100%; use estimation to assign probabilities that events occur in a given context, using common fractions, percentages and decimals

  Elaborations

  • recognising that the probability of an event occurring can be represented numerically as either a number ranging from zero to one or a percentage from 0% to 100% where zero or 0% means it will not happen and one or 100% means it is certain to happen
  • using a scale of zero to one or 0% to 100% to estimate chances of events
  • listing the different possible outcomes for rolling a dice and using a scale to locate the relative probability by considering the chance of more than or less than for each possible event, for example, the probability of getting a number greater than 4
  • recognising the language used to describe situations involving uncertainty, such as what it means to be ‘lucky’, a ‘75% chance’ of rain or a ‘1-in-100 years’ flood
  • exploring Aboriginal and/or Torres Strait Islander children’s instructive games, such as Weme from the Warlpiri Peoples of Central Australia, to investigate and assign probabilities that events will occur, indicating their estimated likelihood

  VC2M6P01 | Mathematics | Mathematics Version 2.0 | Level 6 | Probability

• VC2M7N01

  describe the relationship between perfect square numbers and square roots, and use squares of numbers and square roots of perfect square numbers to solve problems

  Elaborations

  • investigating squares of natural numbers from one to 20, and connecting them to visual representations such as dots arranged in a square pattern
  • using the square and square root notation, and the distributive property and area diagrams, to calculate the squares of two-digit numbers; for example, 432=40+32=402+2×40×3+32=1600+240+9=1849
  • determining between which 2 consecutive natural numbers the square root of a given number lies; for example, 43 is between the square numbers 36 and 49 so 43 is between 36 and 49 and therefore between 6 and 7
  • generating a list of perfect square numbers and describing any emerging patterns, for example, the last digit of perfect square numbers, or the difference between consecutive square numbers, and recognising the constant second difference
  • using the relationship between perfect square numbers and their square roots to determine the perimeter of a square tiled floor using square tiles; for example, an area of floor with 144 square tiles has a perimeter of 48 tile lengths

  VC2M7N01 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M8N02

  establish and apply the exponent laws with positive integer exponents and the zero exponent, using exponent notation with numbers

  Elaborations

  • recognising the connection between exponent form and expanded form with the exponent laws of product of powers rule, quotient of powers rule, and power of a power rule, for example, 23×22 can be represented as 2×2×2×2×2=25 , and connecting the result to the addition of exponents
  • applying the exponent laws of the product of powers rule, quotient of powers rule, power of a power rule and zero exponent individually and in combination; for example, using exponents to determine the effect on the volume of a 2 centimetre cube when the cube is enlarged to a 6 centimetre cube, 6323= 23×3323=33, so the volume is increased by a factor of 27
  • using digital tools to systematically explore the application of the exponent laws; observing that the bases need to be the same
  • using examples such as 3434=1, and 34-4=30 to illustrate the necessity that for any non-zero natural number n,  n0=1

  VC2M8N02 | Mathematics | Mathematics Version 2.0 | Level 8 | Number

• 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

• VC2M2N05

  multiply and divide by one-digit numbers using repeated addition, equal grouping, arrays and partitioning to support a variety of calculation strategies

  Elaborations

  • making and naming arrays and using bar models to solve simple multiplication or sharing problems; for example, making different arrays to represent 12 and naming them as ‘3 fours’, ‘2 sixes’, ‘4 threes’ and ‘6 twos’, using physical or virtual materials to make arrays or using bar models to demonstrate that ‘3 fours’ is equal to ‘4 threes’
  • finding the total number represented in an array by partitioning the array using subitising and number facts; for example, describing how they determined the total number of dots arranged in a ‘3 fives’ array by saying, ‘I saw 2 fives, which is 10, and then 5 more, which makes 15’
  • recognising problems that can be solved using division and identifying the difference between dividing a set of objects into 3 equal groups and dividing the same set of objects into groups of 3
  • using a Think Board to solve partition and quotition division problems; for example, sharing a prize of $36 between 4 people, using materials, a diagram and skip counting to find the answer, and explaining whether the answer ‘9’ refers to people or dollars
  • using materials or diagrams, and skip counting, to solve repeated equal-quantity multiplication problems; for example, writing a repeated addition number sentence and using skip counting to solve the problem ‘Four trays of biscuits with 6 on each tray – how many biscuits are there?’

  VC2M2N05 | Mathematics | Mathematics Version 2.0 | Level 2 | 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

• VC2M7N08

  compare, order and solve problems involving addition and subtraction of integers

  Elaborations

  • using less-than and greater-than notation in expressions when comparing and ordering integers; for example, negative 5 is less than positive 2 and can be represented as -5<+2; -3>-6
  • discussing language such as ‘addition’, ‘subtraction’, ‘magnitude’, ‘difference’ and ‘sign’ and synonyms of these terms
  • ordering, adding and subtracting integers using a number line

  VC2M7N08 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M4M03

  solve problems involving the duration of time including situations involving ‘am’ and ‘pm’ and conversions between units of time

  Elaborations

  • calculating the amount of time between 2 events, such as the start and finish of a movie, a bus journey or a flight, including cases where the starting and finishing times are written using ‘am’ and ‘pm’ notation
  • converting units of time using relationships between units, such as 60 minutes in an hour and 60 seconds in a minute, to solve problems; for example, creating a daily timetable for an activity such as an athletics carnival or planning an exercise routine with activities and rests
  • exploring Aboriginal and/or Torres Strait Islander Peoples’ explanations of the passing of time through cultural accounts about cyclic phenomena involving the sun, moon and stars

  VC2M4M03 | Mathematics | Mathematics Version 2.0 | Level 4 | Measurement

• VC2M1N02

  partition one- and two-digit numbers in different ways using physical and virtual materials, including partitioning two-digit numbers into tens and ones

  Elaborations

  • building knowledge and understanding of the part-part-whole facts to 10, using physical and virtual materials; for example, using virtual ten-frames through a digital app or website to identify pairs of numbers that combine to make 10
  • using physical and virtual materials to partition numbers into counts of tens and ones; for example, recognising 35 as 3 tens and 5 ones or as 2 tens and 15 ones
  • using part-part-whole reasoning and physical or virtual materials to represent 24, then partitioning 24 in different ways and recording the partitions using numbers; for example, 10, 10 and 4 combine to make 24 or 10 and 14 combine to make 24

  VC2M1N02 | Mathematics | Mathematics Version 2.0 | Level 1 | Number

• VC2M1N06

  use mathematical modelling to solve practical problems involving equal sharing and grouping; represent the situations with diagrams, physical and virtual materials, and use calculation strategies to solve the problem

  Elaborations

  • modelling problems involving repeated equal group situations, such as ‘How many wheels are needed for 3 cars?’, using materials and drawing a picture to show what they did, and recording the results with a number
  • modelling practical problems involving equal sharing situations; for example, sharing a set of dominoes between the 2 players in a game, and then counting or subitising to ensure they both have the same number of tiles
  • modelling money problems involving equal sharing; for example, sorting coins from a moneybox according to their denominations, sharing the coins equally between 4 people, and using counting or subitising to ensure they have equal amounts of each denomination

  VC2M1N06 | Mathematics | Mathematics Version 2.0 | Level 1 | Number

• 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

• VC2M10ST03

  construct two-way tables and discuss possible relationship between categorical variables

  Elaborations

  • using two-way tables to investigate and comparing the survey responses to questions involving five-point Likert scale against 2 different categories of respondents, for example, junior students’ responses compared to senior students’ responses to a survey question
  • recording data in two-way tables and using percentages and proportions to identify patterns and associations in the data
  • conducting a litter survey around the school, considering the relationship between different categorical variables such as the day of the week (as canteen specials might lead to different types of litter) or the weather (due to hot days leading to more icy poles and cold drinks being sold)

  VC2M10ST03 | Mathematics | Mathematics Version 2.0 | Level 10 | Statistics

• VC2M4A02

  recall and demonstrate proficiency with multiplication facts up to 10 × 10 and related division facts, and explain the patterns in these; extend and apply facts to develop efficient mental and written strategies for computation with larger numbers without a calculator

  Elaborations

  • using arrays on grid paper or created with blocks or counters to develop, represent and explain patterns in multiplication facts up to 10 × 10; and using the arrays to explain the related division facts
  • using materials or diagrams to develop and record multiplication strategies such as doubling, halving, commutativity and adding one more or subtracting from a group to reach a known fact; for example, creating multiples of 3 on grid paper and doubling to find multiples of 6, and recording and explaining the connections to the × 3 and × 6 multiplication facts: 3, 6, 9, … doubled is 6, 12, 18, …
  • using known multiplication facts for 2, 3, 5 and 10 to establish multiplication facts for 4, 6, 7, 8 and 9 in different ways; for example, using multiples of 10 to establish the multiples of 9 as ‘to multiply a number by 9 you multiply by 10 then take the number away’: 9 × 4 = 10 × 4 − 4, so 9 × 4 is 40 − 4 = 36; or using multiples of 3 as ‘to multiply a number by 9 you multiply by 3, and then multiply the result by 3 again’
  • using arrays and known multiplication facts for twos and fives to develop the multiplication facts for sevens, applying the distributive property of multiplication; for example, when finding 6 × 7, knowing that 7 is made up of 2 and 5, and using an array to show that 6 × 7 is the same as 6 × 2 + 6 × 5 = 12 + 30, which is 42

  VC2M4A02 | Mathematics | Mathematics Version 2.0 | Level 4 | Algebra

• VC2M1N04

  add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies

  Elaborations

  • using drawings, physical and virtual materials, and number combinations within 10 to add and subtract collections to 20
  • adding and subtracting numbers within 20, using a variety of representations and strategies, such as counting on, counting back, partitioning and part-part-whole knowledge of numbers to 10; for example, using partitioning and combining 7+5=7+3+2=10+2=12
  • developing and using strategies for one-digit addition and subtraction based on part-part-whole relationships for each of the numbers to 10 and subitising with physical and virtual materials; for example, 8 and 6 is the same as 8 and 2 and 4
  • representing story problems involving addition and subtraction of numbers within 20 using a Think Board; recognising and using + and − symbols and the equal sign (=) to represent the operations of addition and subtraction; and showing and explaining the connections between any materials used using the language of plus and minus, and the numbers within the story problem
  • creating and performing addition and subtraction stories told through Aboriginal and/or Torres Strait Islander dances

  VC2M1N04 | Mathematics | Mathematics Version 2.0 | Level 1 | Number