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• VC2M2A01

  recognise, describe and create additive patterns that increase or decrease by a constant amount, using numbers, shapes and objects, and identify missing elements in the pattern

  Elaborations

  • creating a pattern sequence with materials, writing the associated number sequence, and then describing the sequence so someone else can replicate it with different materials; for example, using matchsticks or toothpicks to create a growing pattern of triangles – using 3 for one triangle, 5 for 2 triangles, 7 for 3 triangles – and describing the pattern as ‘Start with 3 and add 2 each time’
  • recognising patterns in the built environment to locate additive pattern sequences (for example, responding to ‘How many windows in one train carriage, 2 train carriages, 3 train carriages …?’ or ‘How many wheels on one car, 2 cars, 3 cars …?’) and recording the results in a diagram or table
  • recognising the constant term being added or subtracted in an additive pattern and using it to identify missing elements in the sequence
  • recognising additive patterns in the environment on Country/Place and in Aboriginal and/or Torres Strait Islander material culture; and representing these patterns using drawings, coloured counters and numbers

  VC2M2A01 | Mathematics | Mathematics Version 2.0 | Level 2 | Algebra

• 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

• Mathematics | Mathematics: Learning in Mathematics

  The proficiencies of Understanding, Fluency, Problem Solving and Reasoning are fundamental to learning mathematics and working mathematically and are applied across all three strands Number and Algebra, Measurement and Geometry, and Statistics and Probability.

  Understanding refers to students...

  Overview material | Mathematics

• 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

• VCMMG366

  Prove and apply angle and chord properties of circles

  Elaborations

  • performing a sequence of steps to determine an unknown angle or length in a diagram involving a circle, or circles, giving a justification in moving from one step to the next
  • communicating a proof using a logical sequence of statements
  • proving results involving chords of circles

  VCMMG366 | Mathematics | Level 10A | Measurement and Geometry | Geometric reasoning

• VCMMG288

  Investigate the relationship between features of circles such as circumference, area, radius and diameter. Use formulas to solve problems involving determining radius, diameter, circumference and area from each other

  Elaborations

  • investigating the circumference and area of circles with materials or by measuring, to establish an understanding of formulas
  • investigating the area of circles using a square grid or by rearranging a circle divided into sectors
  • solving problems given one of radius, diameter, circumference or area of a circle, then the other quantities are determined from this

  VCMMG288 | Mathematics | Level 8 | Measurement and Geometry | Using units of measurement

• 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

• VCMNA277

  Solve a range of problems involving rates and ratios, including distance-time problems for travel at a constant speed, with and without digital technologies

  Elaborations

  • understanding that rate and ratio problems can be solved using fractions or percentages and choosing the most efficient form to solve a particular problem
  • calculating population growth rates in Australia and Asia and explaining their difference
  • finding one of distance travelled, time taken or average speed given the other two quantities

  VCMNA277 | Mathematics | Level 8 | Number and Algebra | Real numbers

• VC2M2ST02

  create different graphical representations of data using software where appropriate; compare the different representations, and identify and describe common and distinctive features in response to questions

  Elaborations

  • collecting data from a limited list of choices, creating 2 different graphical representations of the data, and discussing and comparing the different representations; for example, asking the class to choose their favourite colour from a given set, then co-creating a picture graph with colours on the horizontal axis and comparing it to a column graph with colours on the horizontal axis and numbers on the vertical axis
  • creating different data displays (for example, lists, tally charts, jointly created column graphs and picture graphs) to represent a data set, describing the information that each display represents and discussing how easy or hard they are to interpret and why
  • using digital tools to create picture graphs to represent data using one-to-one correspondence, deciding on an appropriate title for the graph and considering whether the categories of data are appropriate for the context
  • comparing picture graphs with one-to-one column graphs of the same data, interpreting the data in each and saying how they are the same and how they are different; for example, collecting data on the country of birth of each student and creating different pictographs to represent classroom data
  • using dot plots, sticker charts, picture graphs, bar charts and column graphs to represent data

  VC2M2ST02 | Mathematics | Mathematics Version 2.0 | Level 2 | Statistics

• VC2M3M04

  describe the relationship between the hours and minutes on analog and digital clocks, and read the time to the nearest minute

  Elaborations

  • representing and reading the time on an analog clock using the markings and the positions of the hands, to the nearest minute mark or 5-minute interval
  • reading and connecting analog and digital time, interpreting times, and recognising and using the language of time, for example, 12:15 as a quarter past 12, or 15 minutes past 12; 12:45 as a quarter to one or 15 minutes before one o’clock; and 10:05 as 5 minutes past 10
  • reading analog clocks throughout the day, and noticing and connecting the position of the hour hand and the distance the minute hand has travelled during the current hour

  VC2M3M04 | Mathematics | Mathematics Version 2.0 | Level 3 | Measurement

• 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

• 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

• VC2M8SP01

  identify the conditions for congruence and similarity of triangles and explain the conditions for other sets of common shapes to be congruent or similar, including those formed by transformations

  Elaborations

  • developing an understanding of what it means for shapes to be congruent or similar
  • using the enlargement transformation and digital tools to develop sets of similar shapes
  • investigating sufficient conditions to establish that 2 triangles are congruent
  • applying logical reasoning and tests for congruence and similarity, to problems and proofs involving plane shapes
  • comparing angle and side measurements of shapes under transformation to answer questions such as ‘What changes?’ and ‘What stays the same?’
  • establishing that 2 shapes are congruent if one lies exactly on top of the other after one or more transformations, including translations, reflections and rotations, and recognising that the matching sides and the matching angles are equal

  VC2M8SP01 | Mathematics | Mathematics Version 2.0 | Level 8 | Space

• VC2M6A01

  recognise and use rules that generate visually growing patterns and number patterns involving rational numbers

  Elaborations

  • investigating patterns such as the number of tiles in a geometric pattern, or the number of dots or other shapes in successive repeats of a strip or border pattern, looking for patterns in the way the numbers increase or decrease
  • using a calculator or spreadsheet to experiment with number patterns that result from multiplying or dividing; for example, 1 ÷ 9, 2 ÷ 9, 3 ÷ 9 …, 210 × 11, 211 × 11, 212 × 11 …, 111 × 11, 222 × 11, 333 × 11 …, or 100 ÷ 99, 101 ÷ 99, 102 ÷ 99 …
  • creating an extended number sequence that represents an additive pattern using decimals; for example, representing the additive pattern formed as students pay their $2.50 for an incursion as 2.50, 5.00, 7.50, 10.00, 12.50, 15.00, 17.50 …
  • investigating the number of regions created by successive folds of a sheet of paper (one fold, 2 regions; 2 folds, 4 regions; 3 folds, 8 regions) and describing the pattern using everyday language
  • creating a pattern sequence with materials, writing the associated number sequence and then describing the sequence with a rule so someone else can replicate it with different materials; for example, using matchsticks or toothpicks to create a growing pattern of triangles using 3 for one triangle, 5 for 2 triangles and 7 for 3 triangles and describing the pattern as ‘Multiply the number of triangles by 2 and then add one for the extra toothpick in the first triangle’

  VC2M6A01 | Mathematics | Mathematics Version 2.0 | Level 6 | Algebra

• VC2M8M02

  solve problems involving the volume and capacity of right prisms using appropriate units

  Elaborations

  • using models to demonstrate the number of cubic centimetres in a cubic metre and relating this to capacities of millilitres and litres, recognising that one millilitre is equivalent to one cm³
  • solving practical problems involving volume and capacity, for example, optimal packaging and production
  • choosing which measurements are useful to consider when solving practical problems in context; for example, when purchasing a new washing machine, the dimensions are useful when determining whether it will fit in the available space in the laundry and its capacity is useful when considering the maximum washing load it can carry
  • investigating, reasoning and finding solutions to measurement problems involving dimensions, rates, volume and capacity of objects; for example, given the dimensions of a pool and the rate of flow from a tap, determining how long it will take to fill the pool to its normal capacity

  VC2M8M02 | Mathematics | Mathematics Version 2.0 | Level 8 | Measurement

• 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

• VC2M3P01

  identify practical activities and everyday events that involve chance, and describe possible outcomes and events as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’, explaining reasoning

  Elaborations

  • predicting what could happen next in practical activities that involve an element of chance, considering possible outcomes and using terms such as ‘likely’ or ‘unlikely’ to explain their predictions
  • classifying a list of everyday events or sorting a set of event cards according to how likely they are to happen, using the language of chance and giving reasons for classifications; and discussing how impossible outcomes cannot ever happen, and uncertain outcomes are affected by chance as they may or may not happen, whereas certain events must always happen so they are not affected by chance
  • making predictions and testing what would happen, for example, if 10 names were put in a box and names were then drawn out one at a time and replaced after each selection, discussing how likely it would be after 10 selections that all 10 names were drawn from the box or that one name was drawn multiple times

  VC2M3P01 | Mathematics | Mathematics Version 2.0 | Level 3 | Probability

• VC2M2SP02

  locate positions in two-dimensional representations of a familiar space; move positions by following directions and pathways

  Elaborations

  • interpreting maps of familiar places and identifying the position of key features
  • understanding that we use maps to receive and give directions and to describe place and spatial relationships between places
  • using a classroom seating plan to locate a new seating position and giving directions to other classmates to find their seats
  • following and creating movement instructions that need to be carried out to move through a 4 × 4 grid mat on the classroom floor or on a computer screen, for example, one forward, 2 to the right and one backwards and so on to reach a target square; or using a robotic toy to follow a path on a street scene on a floor mat, adjusting their instructions to the robot toy as they consider the order of their instructions, the direction and how far they want the toy to travel
  • moving around a two-dimensional maze using directional language to describe turns and changes in direction, including saying, for example, ‘clockwise’, ‘anticlockwise’, ‘quarter turn to the left’ and ‘take the path to the right’

  VC2M2SP02 | Mathematics | Mathematics Version 2.0 | Level 2 | Space

• VCMMG345

  Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes

  Elaborations

  • distinguishing between a practical demonstration and a proof (for example demonstrating triangles are congruent by placing them on top of each other, as compared to using congruence tests to establish that triangles are congruent)
  • performing a sequence of steps to determine an unknown angle giving a justification in moving from one step to the next.
  • communicating a proof using a sequence of logically connected statements

  VCMMG345 | Mathematics | Level 10 | Measurement and Geometry | Geometric reasoning