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• VC2M5N06

  solve problems involving multiplication of larger numbers by one- or two-digit numbers, choosing efficient mental and written calculation strategies and using digital tools where appropriate; check the reasonableness of answers

  Elaborations

  • solving multiplication problems such as 253 × 4 using a doubling strategy, for example, 2 × 253 = 506 and 2 × 506 = 1012
  • solving multiplication problems like 15 × 16 by thinking of factors of both numbers, 15 = 3 × 5, 16 = 2 × 8, and rearranging the factors to make the calculation easier, 5 × 2 = 10, 3 × 8 = 24 and 10 × 24 = 240
  • using an array to show place value partitioning to solve multiplication, such as 324 × 8, thinking 300 × 8 = 2400, 20 × 8 = 160, 4 × 8 = 32 then adding the parts, 2400 + 160 + 32 = 2592; and connecting the parts of the array to a standard written algorithm
  • using different strategies used to multiply numbers, and explaining how they work and if they have any limitations; for example, discussing how the Japanese visual method for multiplication is not effective for multiplying larger numbers

  VC2M5N06 | Mathematics | Mathematics Version 2.0 | Level 5 | 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

• VCMNA242

  Compare fractions using equivalence. Locate and represent positive and negative fractions and mixed numbers on a number line

  Elaborations

  • exploring equivalence among families of fractions by using a fraction wall or a number line (for example by using a fraction wall to show that 2/3 is the same as 4/6 and 6/9)

  VCMNA242 | Mathematics | Level 7 | Number and Algebra | Real numbers

• VCMNA094

  Recognise the importance of repetition of a process in solving problems

  Elaborations

  • using one-to-one correspondence to determine which of two sets is larger, or if they are of equal size
  • dividing a set of blocks in a simple ratio such as ‘2 for me’, ‘1 for you’

  VCMNA094 | Mathematics | Level 1 | Number and Algebra | Patterns and algebra

• Mathematics: Level 1 achievement standards

  Number and Algebra

  Students count to and from 100 and locate these numbers on a number line. They partition numbers using place value and carry out simple additions and subtractions, using counting strategies. Students recognise Australian coins according to their value. They identify representations...

  Level description | Mathematics | Level 1

• Mathematics Version 2.0: Level 2 achievement standards

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

  Level description | Mathematics | Mathematics Version 2.0 | Level 2

• Mathematics Version 2.0: Level 10 description

  In Level 10, learning in Mathematics builds on each student’s prior learning and experiences and provides the basis for a sound background in number, algebra, function, geometry and statistics. Students engage in a range of approaches to the learning and doing of mathematics that...

  Level description | Mathematics | Mathematics Version 2.0

• VC2M9ST01

  analyse reports of surveys in digital media and elsewhere for information on how data was obtained around everyday questions and issues involving at least one numerical and at least one categorical variable, to estimate population means and medians

  Elaborations

  • investigating and evaluating statistical reports in the media and other places by linking claims to displays, statistics and representative data
  • investigating the use of statistics in reports regarding the growth of Australia’s trade with other countries of the Asia region
  • investigating a range of data and its sources, for example, the age of residents in Australia, Cambodia and Tonga, or the number of subjects studied at school in a year by 14-year-old students in Australia, Singapore, Japan, South Korea and Timor-Leste
  • analysing reports of public opinion surveys on environmental issues, such as land clearing, wind farms or single-use plastics, discussing methods of data collection and the reasonableness of any inferences made
  • comparing the annual rainfall in various parts of Australia, Pakistan, New Guinea and Malaysia

  VC2M9ST01 | Mathematics | Mathematics Version 2.0 | Level 9 | Statistics

• VC2M2A03

  recall and demonstrate proficiency with multiplication facts for twos; extend and apply facts to develop the related division facts using doubling and halving

  Elaborations

  • recognising and relating terms such as ‘double’, ‘twice’ and ‘multiply by 2’, and ‘halve’ and ‘divide by 2’ using physical and virtual materials; for example, colouring numbers on a hundreds chart to represent doubles and using it to recognise halves or recognising the doubling pattern and applying the pattern to find related facts such as ‘For 8 twos, think 2 eights’
  • doubling and halving collections to practise and develop fluency with multiplication and division facts for twos, leading to recall of these facts
  • establishing an understanding of doubles and near doubles using physical or virtual manipulatives; for example, using manipulatives to establish that doubling 5 gives you 10, then extending this doubling fact to respond to the question ‘How can you use this fact to double 6 or double 4?’
  • developing fluency with doubling and halving numbers within 20 using physical or virtual materials and playing doubling and halving games; for example, using a physical or virtual dice and choosing whether to double or halve to reach a target number 

  VC2M2A03 | Mathematics | Mathematics Version 2.0 | Level 2 | Algebra

• VC2M3N01

  identify, explain and use the properties of odd and even numbers

  Elaborations

  • identifying even numbers using skip counting by twos or by grouping even collections of objects in twos
  • explaining why all numbers that end in the digits 0, 2, 4, 6 and 8 are even and that numbers ending in 1, 3, 5, 7 and 9 are odd
  • explaining why some materials can be shared evenly between 2 people without leaving a remainder and some cannot
  • explaining the patterns involved in adding, subtracting and multiplying odd and even numbers (for example, even + even = even, odd + even = odd, odd + odd = even) and using this to decide whether answers to addition, subtraction and multiplication calculations are correct or not
  • following an algorithm consisting of a flow chart with a series of instructions and decisions to determine whether a number is even or odd; and using the algorithm to identify which elements of a set of numbers are divisible by 2

  VC2M3N01 | Mathematics | Mathematics Version 2.0 | Level 3 | Number

• VC2M2N02

  partition, rearrange, regroup and rename two- and three-digit numbers using standard and non-standard groupings; recognise the role of a zero digit in place value notation

  Elaborations

  • comparing the digits of a number with materials grouped into hundreds, tens and ones, and explaining the meaning of each of the digits in the materials
  • renaming numbers in different ways using knowledge of place value; for example, renaming 245 as 24 tens and 5 ones or 2 hundreds and 45 ones

  VC2M2N02 | Mathematics | Mathematics Version 2.0 | Level 2 | Number

• VCMNA103

  Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences

  Elaborations

  • developing fluency and confidence with numbers and calculations by saying number sequences
  • recognising that the natural numbers with zero form an ordered infinite set {0, 1, 2, 3 … } with a first element but no last element
  • recognising patterns in number sequences, such as adding 10 always results in the same final digit

  VCMNA103 | Mathematics | Level 2 | Number and Algebra | Number and place value

• VCMNA129

  Investigate the conditions required for a number to be odd or even and identify odd and even numbers

  Elaborations

  • identifying even numbers using skip counting by twos or by grouping even collections of objects in twos
  • explaining why all numbers that end in the digits 0, 2, 4, 6 and 8 are even and that numbers ending in 1, 3, 5, 7 and 9 are odd

  VCMNA129 | Mathematics | Level 3 | Number and Algebra | Number and place value

• 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

• VC2M6A03

  design and use algorithms involving a sequence of steps and decisions that use rules to generate sets of numbers; identify, interpret and explain emerging patterns

  Elaborations

  • using an algorithm to create extended number sequences involving rational numbers, using a rule and digital tools, and explaining any emerging patterns
  • designing an algorithm to model operations, using the concept of input and output, describing and explaining relationships and any emerging patterns; for example, using function machines to model operations and recognising and comparing additive and multiplicative relationships
  • designing an algorithm or writing a simple program to generate a sequence of numbers based on the user’s input and a chosen operation, discussing any emerging patterns; for example, generating a sequence of numbers and comparing how quickly the sequences are growing in comparison to each other using the rule ‘add 2 to the input number’ compared to multiplying the input number by 2

  VC2M6A03 | Mathematics | Mathematics Version 2.0 | Level 6 | Algebra

• VC2M2M04

  recognise and read the time represented on an analog clock to the hour, half-hour and quarter hour

  Elaborations

  • creating an analog clock from a paper plate, showing the placement of the numbers and the 2 hands, and explaining how long it takes for the 2 hands to move around the clock face and what time unit each is showing
  • recognising and describing the relationship between the movement of the hands on an analog clock and the duration of time it represents; for example, connecting the language of ‘half past’ to mean when the ‘big hand’ will be at half past the hour and recognising this position as being halfway around its full cycle
  • dividing a clock face into halves and quarters, and connecting the subdivisions with telling the time to the half-hour and quarter hour; and explaining the meaning of ‘quarter past’ and ‘quarter to’ referring to the hour

  VC2M2M04 | Mathematics | Mathematics Version 2.0 | Level 2 | Measurement

• VC2M8M03

  solve problems involving the circumference and area of a circle using formulas and appropriate units

  Elaborations

  • deducing that the area of a circle is between 2 radius squares and 4 radius squares, and using 3 × radius² as a rough estimate for the area of a circle
  • investigating the area of circles using a square grid or by rearranging a circle divided into smaller and smaller sectors or slices to resemble a close approximation of a rectangle
  • applying the formulas for the area and circumference of a circle to solve practical problems, and using one of the measures of radius, diameter, circumference or area to deduce the value of the other measures; for example, determining the length of material needed to edge a round table, given its dimensions as the area of the tabletop
  • exploring traditional weaving designs by Aboriginal and Torres Strait Islander Peoples and investigating the significance and use of circles

  VC2M8M03 | Mathematics | Mathematics Version 2.0 | Level 8 | Measurement

• 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

• 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