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• VC2M10A09

  solve simultaneous linear equations, using algebraic and graphical techniques including using digital tools

  Elaborations

  • investigating situations involving simultaneous linear equations in context (such as multiple quotes for a job, or profit and loss) and solving the equations graphically, giving solutions in everyday language (such as ‘break-even point’ or ‘point to change providers’ for the job)
  • describing the solution of simultaneous equations within the context of the situation
  • using the algebraic methods of substitution and elimination, with and without the use of digital tools, and identifying which technique is the most efficient for a given pair of equations
  • associating the solution of simultaneous equations with the coordinates of the intersection of their corresponding graphs
  • investigating the strategies inherent in Aboriginal and/or Torres Strait Islander children’s instructive games, for example, Weme from the Warlpiri Peoples of central Australia, and their connection to strategies to solve simultaneous linear equations in 2 variables

  VC2M10A09 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M2A04

  apply repetition in arithmetic operations, including multiplication as repeated addition and division as repeated subtraction

  Elaborations

  • using technology to construct a sequence of numbers based on constant addition or subtraction from a given starting value
  • sharing a set of objects equally between a small number of groups

  VC2M2A04 | Mathematics | Mathematics Version 2.0 | Level 2 | Algebra

• 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

• VC2M10AP01

  explore counting principles, and factorial notation as a representation that provides efficient counting in multiplicative contexts, including calculations of probabilities

  Elaborations

  • applying the multiplication principle to problems involving combinations including probabilities relating to sampling with and without replacement, and representing these using tree diagrams
  • understanding that a set with n elements has 2ⁿ different subsets formed by considering each element for inclusion or not in combination, and that these can be systematically listed using a tree diagram or a table; for example, the set {a, b, c} has 2³ = 8 subsets which are { ∅, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}
  • using the definition of $n$! to represent and calculate in contexts that involve choices from a set; for example, how many different combinations of 3 playing cards from a pack? How many if the suits are ignored? How many with and without replacement?
  • performing calculations on numbers expressed in factorial form, such as $\frac{n!}{r!}$ to evaluate the number of possible arrangements of $n$ objects in a row, $r$ of which are identical; for example, 5 objects, 3 of which are identical, can be arranged in a row in
    $\frac{5!}{3!}=\frac{5\times 4\times 3\times 2\times 1}{3\times 2\times 1}=\mathrm{ }$20 different ways

  VC2M10AP01 | Mathematics | Mathematics Version 2.0 | Level 10A | Probability

• VC2MFM01

  identify and compare attributes of objects and events, including length, capacity, mass and duration, use direct comparisons and communicate reasoning

  Elaborations

  • using language to describe the measurement attributes of length, mass, capacity and duration, and connecting the words with the appropriate attribute; for example, using words like ‘tall’, ‘short’, ‘wide’, ‘long’ and ‘high’ to describe the attribute of length
  • directly comparing pairs of objects to say which is longer/shorter, and explaining or demonstrating how they know; for example, standing back-to-back to determine who is taller or choosing to line up the bases of a spoon and fork to decide which is longer and explaining why
  • starting 2 events at the same time to decide which takes longer; for example, putting on a pair of sandals with buckles or Velcro, describing the duration using familiar terms and reasoning, ‘I took a longer time because I’m still learning to do up my buckles’
  • directly comparing pairs of everyday objects from the kitchen pantry to say which is heavier/lighter; for example, hefting a tin of baked beans and a packet of marshmallows or comparing the same pair of objects to say which is longer/shorter and discussing comparisons

  VC2MFM01 | Mathematics | Mathematics Version 2.0 | Foundation Level | Measurement

• VC2MFM02

  sequence days of the week and times of the day, including morning, lunchtime, afternoon and night-time, and connect them to familiar events and actions

  Elaborations

  • ordering images of daily events on a string line across the room, and justifying the placement by referring to morning, lunchtime, afternoon and night-time
  • distinguishing between the days of the school week and weekends, and recognising that the days of the week form a sequence that repeats, with Monday always following on from Sunday
  • sequencing the events from a story in the order in which they occurred, using language like ‘this happened first’ then ‘this happened next’
  • creating, interpreting and discussing classroom rosters, for example, a roster for watering the classroom garden, and asking, ‘Who watered the garden yesterday?’ or ‘Whose turn is it today?’
  • creating a pictorial diary to show the important events that happen on the various days of the week

  VC2MFM02 | Mathematics | Mathematics Version 2.0 | Foundation Level | Measurement

• 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

• VC2M7M02

  solve problems involving the volume of right prisms including rectangular and triangular prisms, using established formulas and appropriate units

  Elaborations

  • building a rectangular prism out of unit cubes and showing that the measure of volume is the same as would be found by multiplying the 3 edge lengths or by multiplying the area of the base by the height/length
  • developing the connection between the area of the parallel cross-section (base), the height and the volume of a rectangular or triangular prism to other prisms
  • connecting the area of the floor space and the number of floors of a high-rise building to calculate the volume of a building
  • using dynamic geometry software, spatial reasoning and prediction to derive the formula for the volume of prisms

  VC2M7M02 | Mathematics | Mathematics Version 2.0 | Level 7 | Measurement

• 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

• VC2M5M04

  estimate, construct and measure angles in degrees, using appropriate tools, including a protractor, and relate these measures to angle names

  Elaborations

  • using a protractor to measure angles in degrees and classifying these angles using angle names; for example, an acute angle is less than 90°, an obtuse angle is more than 90° and less than 180°, a right angle is equal to 90° and a reflex angle is more than 180° and less than 360°
  • estimating the size of angles in the environment using a clinometer and describing the angles using angle names
  • using a ruler and protractor to construct triangles, given the angle measures and side lengths
  • using a protractor to measure angles when creating a pattern or string design within a circle
  • recognising the size of angles within shapes that do and do not tessellate, measuring the angles and using the sum of angles to explain why some shapes will tessellate and other shapes do not

  VC2M5M04 | Mathematics | Mathematics Version 2.0 | Level 5 | Measurement

• VC2M3M03

  recognise and use the relationship between formal units of time, including days, hours, minutes and seconds, to estimate and compare the duration of events

  Elaborations

  • estimating how long it would take to read a set passage of text, and sharing this information to demonstrate understanding of formal units of duration of time
  • planning a sequence of events based on estimates of the duration of each event; for example, planning a set of activities for a class party by estimating how long each game or activity will take
  • reading or setting the time on digital devices to the minute or second; for example, setting an online timing device to count down from a set time, or setting the time on a digital clock
  • using sand timers and digital timers to measure and check estimates of short durations of time, such as one minute, 3 minutes and 5 minutes
  • exploring how cultural accounts of Aboriginal and Torres Strait Islander Peoples explain cycles of time that involve the sun, moon and stars

  VC2M3M03 | Mathematics | Mathematics Version 2.0 | Level 3 | Measurement

• 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

• VC2M5N08

  check and explain the reasonableness of solutions to problems, including financial contexts using estimation strategies appropriate to the context

  Elaborations

  • interpreting a series of contextual problems to decide whether an exact answer or an approximate calculation is appropriate, and explaining their reasoning in relation to the context and the numbers involved
  • recognising the effect of rounding addition, subtraction, multiplication and division calculations, and rounding both numbers up, both numbers down, and one number up and one number down; and explaining which estimation is the best approximation and why
  • considering the type of rounding that is appropriate when estimating the amount of money required; for example, rounding up or rounding down when buying one item from a store using cash, compared to rounding up the cost of every item when buying groceries to estimate the total cost and not rounding when the financial transactions are digital

  VC2M5N08 | Mathematics | Mathematics Version 2.0 | Level 5 | Number

• VC2M4N07

  choose and use estimation and rounding to check and explain the reasonableness of calculations, including the results of financial transactions

  Elaborations

  • using proficiency with basic facts to estimate the result of a calculation and say what amounts the answer will be between; for example, 5 packets of biscuits at $2.60 each will cost between $10 and $15 as 5 × $2 = $10 and 5 × $3 = $15
  • using rounded amounts to complete an estimated budget for a shopping trip or an excursion, explaining why overestimating the amounts is appropriate
  • recognising the effect of rounding in addition and multiplication calculations; rounding both numbers up, both numbers down, and one number up and one number down, and explaining which is the best approximation and why

  VC2M4N07 | Mathematics | Mathematics Version 2.0 | Level 4 | Number

• VC2M8N05

  solve problems involving the use of percentages, including percentage increases and decreases and percentage error, with and without digital tools

  Elaborations

  • using percentages to solve problems, including those involving mark-ups, discounts and Goods and Services Tax (GST)
  • using percentages to calculate population increases and decreases
  • using percentage error to compare the relative size of error in calculations involving a given or actual value, and an estimated or measured value

  VC2M8N05 | Mathematics | Mathematics Version 2.0 | Level 8 | Number

• VC2M4N04

  count by multiples of quarters, halves and thirds, including mixed numerals; locate and represent these fractions as numbers on number lines

  Elaborations

  • cutting objects such as oranges or sandwiches into quarters and counting by quarters to find the total number, and saying the counting sequence ‘one-quarter, two-quarters, three-quarters, four-quarters or one-whole, five-quarters or one-and-one-quarter, six-quarters or one-and-two-quarters … eight-quarters or two-wholes ...’
  • subdividing the sections between whole numbers on parallel number lines so that one shows halves, another shows quarters and one other shows thirds; and counting the fractions by jumping along the number lines, and noticing when the count is at the same position on the parallel lines
  • converting mixed numerals into improper fractions and vice versa, and representing mixed numerals on a number line
  • using a number line to represent and count in tenths, recognising that 10 tenths is equivalent to one

  VC2M4N04 | Mathematics | Mathematics Version 2.0 | Level 4 | Number

• VC2M7SP03

  describe the effect of transformations of a set of points using coordinates in the Cartesian plane, including translations, reflections in an axis, and rotations about the origin

  Elaborations

  • using digital tools to transform shapes in the Cartesian plane, describing and recording the transformations
  • describing patterns and investigating different ways to produce the same transformation, such as using 2 successive reflections to provide the same result as a translation
  • experimenting with, creating and re-creating patterns using combinations of translations, reflections and rotations, using digital tools

  VC2M7SP03 | Mathematics | Mathematics Version 2.0 | Level 7 | Space

• VC2M3ST02

  create and compare different graphical representations of data sets, including using software where appropriate; interpret the data in terms of the context

  Elaborations

  • comparing various student-generated data representations and describing their similarities and differences
  • using digital tools and graphing software to construct graphs of data acquired through experiments or observation and interpreting the data and making inferences; for example, graphing data from a science experiment and interpreting the results
  • selecting appropriate formats or layout styles to present data as information, depending on the type of data and the audience; for example, lists, tables, graphs and infographics
  • using newspapers or magazines to find examples of different displays of data, interpreting and describing the information they present

  VC2M3ST02 | Mathematics | Mathematics Version 2.0 | Level 3 | Statistics

• VC2M2N01

  recognise, represent and order numbers to at least 1000 using physical and virtual materials, numerals and number lines

  Elaborations

  • recognising missing numbers on different number lines, for example, a number line with 1800 on one end and 2200 on the other, with every decade numbered
  • recognising and locating the position of pieces within hundreds chart puzzles using knowledge of the order of natural numbers
  • reading and writing numerals, and saying and ordering two-, three- and four-digit numbers using patterns in the number system, including numbers with zeros in different places and numbers that look and sound similar (such as 808, 880, 818 and 881)
  • collecting large quantities of materials for recycling (for example, ring pulls, bottle tops and bread tags) and grouping them into ones, tens and hundreds, and using the materials to show different representations of two- and three-digit numbers

  VC2M2N01 | Mathematics | Mathematics Version 2.0 | Level 2 | Number

• VC2M1N01

  recognise, represent and order numbers to at least 120 using physical and virtual materials, numerals, number lines and charts

  Elaborations

  • reading, writing and naming numerals and ordering two-digit numbers from zero to at least 120, using patterns within the natural number system, including numbers that look and sound similar, for example, 16, 60, 61 and 66
  • using number tracks or positioning a set of numbered cards in the correct order and relative location by pegging them on an empty number line
  • using hundreds charts to build understanding and fluency with numbers; for example, collaboratively building a hundreds chart using cards numbered from zero to 99, or colour-coding the count of tens in a hundreds chart using one colour to represent the number of tens and another to represent the number of ones
  • recognising that numbers are used in all languages and cultures but may be represented differently in words and symbols (for example, through kanji numbers in Japanese and characters in Chinese) and that there are alternative numeration systems (for example, using special characters for 10 and 100 and other multiples of 10 in Japanese and Chinese numeration)

  VC2M1N01 | Mathematics | Mathematics Version 2.0 | Level 1 | Number