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• VCMMG048

  Locate familiar three-dimensional objects in the classroom when they are named

  Elaborations

  • interpreting everyday language of location by following simple directions and communication, for example, move or track an object, feel or follow a path
  • locating familiar environments and objects, for example, classroom, hall, desk

  VCMMG048 | Mathematics | Level C | Measurement and Geometry | Location and transformation

• VCMMG031

  Respond to a simple statement about location or direction

  Elaborations

  • following directional communication used in daily routine, for example, ‘put in’ to finish an activity, ‘sit down’, ‘stand up’ during an activity or program
  • following everyday language of location and direction through modelled daily routines, for example: looking upwards for ‘up’; using rhymes and chants that relate to movement; following a warm-up sequence for work or sport; unpacking their bag; washing their hands and setting up for lunch
  • exploring the concept of ‘inside’ and ‘outside’ during activities by putting objects ‘in’ and ‘out’ of a container and following routines and instructions that involve moving inside and outside locations

  VCMMG031 | Mathematics | Level B | Measurement and Geometry | Location and transformation

• VCMMG012

  Respond to personally relevant routine events

  Elaborations

  • experiencing events and their equipment, staff, and sensory elements
  • experiencing events and their characteristics being represented by images or augmentative and alternative communication (AAC)
  • reacting to routine events with the support of objects, sounds and textures
  • reacting and responding to daily events within the context of a range of practical situations, for example reacting to the bell for lunch time, responding to the timer, staff or an image for maths

  VCMMG012 | Mathematics | Level A | Measurement and Geometry | Using units of measurement

• VCMMG047

  Match familiar two dimensional shapes and three dimensional objects

  Elaborations

  • matching simple three dimensional shapes with similar attributes, for example, different-sized spheres
    • matching simple two dimensional shapes with similar attributes, for example, different-sized spheres
  • recognising the relationship between familiar shapes using insert puzzles

  VCMMG047 | Mathematics | Level C | Measurement and Geometry | Shape

• VCMMG062

  Identify and sequence regular events that occur during the school day and comment on their duration (short/long)

  Elaborations

  • creating and following a visual schedule based on the school day’s events
  • ordering events based on duration, for example, ‘I can do more at lunch time than recess’
  • comparing and labelling events as long, short, quick
  • understanding the purpose of a clock and some of its features
  • using timers and a clock to explore and compare time and duration of events

  VCMMG062 | Mathematics | Level D | Measurement and Geometry | Using units of measurement

• VCMMG010

  Respond to objects based on length

  Elaborations

  • experiencing objects of various lengths
  • experiencing measurement attributes through the use of sensory input and objects
  • reacting to various measurement attributes of familiar objects, and being introduced to the names of those attributes, in the context of everyday experiences

  VCMMG010 | Mathematics | Level A | Measurement and Geometry | Using units of measurement

• VCMMG027

  Compare objects using direct comparison

  Elaborations

  • exploring objects in structured situations based on length
  • matching objects that are from a small field and identical in length
  • showing recognition or preference for an object based on its mass, capacity or length within a range of situations

  VCMMG027 | Mathematics | Level B | Measurement and Geometry | Using units of measurement

• VCMMG063

  Identify the days of the week in sequence

  Elaborations

  • using picture schedules to identify key events of a day and a week
  • using everyday language ‘sometimes’, ‘always’ and never to indicate the likelihood of an event on a day or week
  • using ‘morning routine’ to identify the days and what will occur during the day
  • communicating the days of the week

  VCMMG063 | Mathematics | Level D | Measurement and Geometry | Using units of measurement

• VC2M3N06

  estimate the quantity of objects in collections and make estimates when solving problems to determine the reasonableness of calculations

  Elaborations

  • estimating how much space a grid paper representation of a large number such as 20 200 will take up on the wall and how much paper will be required
  • estimating the number of people in a large gathering (for example, a school assembly) using known numbers (such as how many students per class)
  • choosing which place value they would estimate to for different situations; for example, choosing to estimate to the nearest ten when estimating how many dots on a ladybird or choosing to estimate to the nearest thousand when estimating crowd sizes at a venue
  • checking the reasonableness of an addition calculation by using two- and three-digit numbers to the nearest ten or hundred to estimate; for example, using 200 + 400 = 600 to estimate and check the solution to the calculation 219 + 385

  VC2M3N06 | Mathematics | Mathematics Version 2.0 | Level 3 | Number

• 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

• VC2M1N03

  quantify sets of objects, to at least 120, by partitioning collections into equal groups using number knowledge and skip counting

  Elaborations

  • counting a large collection of items using groups of fives or tens and skip counting to work out how many there are, and recording the amount and connecting the digits in the number to the grouped materials when using groups of 10
  • counting collections of objects, such as pencils or images of birds in a tree, by grouping them in tens to enable efficient counting, and connecting the digits in the number to the groups of tens and ones
  • counting a large collection of Australian $1 coins by stacking them in piles of 10, skip counting in tens and including any leftover coins to determine the total value

  VC2M1N03 | Mathematics | Mathematics Version 2.0 | Level 1 | Number

• VC2M2N03

  recognise and describe one-half as one of 2 equal parts of a whole and connect halves, quarters and eighths through repeated halving

  Elaborations

  • creating halves of a range of collections sets by sharing collections into 2 equal groups; for example, comparing half of a set of 12 washers with half of a set of 8 bolts to identify how they both represent one-half of their respective set
  • creating halves using measurement attributes – for example, explaining that ‘a half is one part out of 2 equal parts of a whole’; equally folding a strip of paper, dividing a lump of playdough or separating a cup of water into 2 equal parts, and then selecting one of the parts and naming it ‘one-half’; or comparing half of a collection of 10 counters with half of a shape or object and explaining how each shows one-half of the respective whole
  • using repeated halving to subdivide shapes and objects in different ways to make corresponding halves, quarters and eighths; naming the parts and comparing the size of them to notice that they are all the same size; and demonstrating that a quarter is a half of a half and that an eighth is a half of a quarter
  • dividing a shape into equal parts and relating the number of parts to the unit fraction; for example, if there are 4 equal parts then each part is one-quarter and if there are 8 equal parts then each is one-eighth

  VC2M2N03 | Mathematics | Mathematics Version 2.0 | Level 2 | Number

• VC2M9N01

  recognise that the real number system includes the rational numbers and the irrational numbers, and solve problems involving real numbers with and without using digital tools

  Elaborations

  • investigating the real number system by representing the relationships between irrational numbers, rational numbers, integers and natural numbers and discussing the difference between exact representations and approximate decimal representations of irrational numbers
  • using a real number line to indicate the solution interval for inequalities of the form ax+b <c ,
    for example, 2x+7<0 ; or of the form ax+b>c , for example, 1.2x-5.4>10.8
  • using positive and negative rational numbers to solve problems, for example, for financial planning such as budgeting
  • solving problems involving the substitution of real numbers into formulas, understanding that solutions can be represented in exact form or as a decimal approximation, such as calculating the area of a circle using the formula A=πr2 and specifying the answer in terms of π as an exact real number; for example, the circumference of a circle with diameter 5 units is 5π units, and the exact area is π(52)2=254π square units, which rounds to 19.63 square units, correct to 2 decimal places
  • investigating the position of rational and irrational numbers on the real number line, using geometric constructions to locate rational numbers and square roots on a number line; for example, 2 is located at the intersection of an arc and the number line, where the radius of the arc is the length of the diagonal of a one-unit square

  VC2M9N01 | Mathematics | Mathematics Version 2.0 | Level 9 | Number

• VC2M6N07

  solve problems that require finding a familiar fraction, decimal or percentage of a quantity, including percentage discounts, choosing efficient calculation strategies with and without digital tools

  Elaborations

  • explaining how 13 of a quantity can be achieved by dividing by 3, and how knowledge of 13 of a quantity can be used to find 23 or 43 of the same quantity, using situations involving money, length, duration, mass or capacity
  • investigating percentage discounts of 10%, 25% and 50% in an online toy sale, using their equivalent decimal representations of 0.10, 0.25 and 0.50 to calculate the amount of discount on sale items, with and without digital tools
  • linking percentages to their decimal equivalent of tenths and hundredths and using these to determine percentage discounts; for example, finding a 30% discount by using its equivalence to 0.3, dividing by 10 and multiplying the result by 3 to give 30%
  • explaining the equivalence between percentages and fractions, for example, 3313 % and 13 , keeping to percentages that are equivalent to fractions with small denominators such as 6623 % and 12.5%
  • representing a situation with a mathematical expression, for example, numbers and symbols such as 14 × 24, that involves finding a familiar fraction or percentage of a quantity; and using mental strategies or a calculator and explaining the result in terms of the situation in question

  VC2M6N07 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• VC2M8N06

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

  Elaborations

  • modelling situations involving weather and environmental contexts, including temperature or sea depths, by applying operations to positive and negative rational numbers, for example, contexts involving average temperature increases and decreases
  • modelling situations that involve percentage increases or decreases and explaining why it is an increase or decrease, such as mark-ups, discounts, Goods and Services Tax (GST), changes in populations or recycling rates
  • modelling situations involving personal income tax, and interpreting tax tables to determine income tax at various levels of income, including overall percentage of income allocated to tax
  • modelling situations involving percentage increase or decrease such as market trends, effects on population, or effects on the environment over extended time periods

  VC2M8N06 | Mathematics | Mathematics Version 2.0 | Level 8 | Number

• VC2M3N09

  follow and create algorithms involving a sequence of steps and decisions to investigate numbers; describe any emerging patterns

  Elaborations

  • following or creating an algorithm to generate number patterns formed by doubling and halving using technology to assist, where appropriate, and identifying and describing emerging patterns
  • following or creating an algorithm that determines whether a given number is a multiple of 2, 5 or 10, identifying and discussing emerging patterns
  • creating an algorithm as a set of instructions that a classmate can follow to generate multiples of 3 using the rule ‘To multiply by 3 you double the number and add on one more of the number’ (for example, for 3 threes, you double 3 and add on 3 to get 9; for 3 fours you double 4 and add one more 4 to get 12 …)
  • creating a sorting algorithm that will sort a collection of 5-cent and 10-cent coins and providing the total value of the collection by applying knowledge of multiples of 5 and 10

  VC2M3N09 | Mathematics | Mathematics Version 2.0 | Level 3 | Number

• 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

• VC2M7N02

  represent natural numbers in expanded notation using powers of 10, and as products of powers of prime numbers using exponent notation

  Elaborations

  • relating the sequences 10, 100, 1000, 10 000 … and 10¹, 10², 10³, 10⁴ …
  • applying and explaining the connections between place value and expanded notations, for example, 7000=7×103 and 3750=3×103+7×102+5×101
  • applying knowledge of factors to strategies for expressing natural numbers as products of powers of prime factors, such as repeated division by prime factors or creating factor trees, for example, 48=6×8=2×3×2×2×2=31×24=3×24
  • developing familiarity with the sequence 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 and powers of 2; the sequence 1, 3, 9, 27, 81, 243, 729 and powers of 3; and the sequence 1, 5, 25, 125, 625 and powers of 5
  • solving problems involving lowest common multiples and greatest common divisors (highest common factors) for pairs of natural numbers by comparing their prime factorisation

  VC2M7N02 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M5N04

  recognise that 100% represents the complete whole and use percentages to describe, represent and compare relative size; connect familiar percentages to their decimal and fraction equivalents

  Elaborations

  • recognising applications of percentages used in everyday contexts, for example, the bar model used for charging devices indicating the percentage of power remaining, and advertising in retail contexts relating to discounts or sales
  • creating a model by subdividing a whole (for example, using 10 × 10 grids to represent various percentage amounts) and recognising complementary percentages (such as 30% and 70%) combine to make 100%
  • creating a model by subdividing a collection of materials, such as blocks or money, to connect decimals and percentage equivalents of tenths and the commonly used fractions 12, 14 and 34; for example, connecting that one-tenth or 0.1 represents 10% and one-half or 0.5 represents 50%, and recognising that 60% of a whole is 10% more of the whole than 50%
  • using physical and virtual materials to represent the relationship between decimal notation and percentages, for example, 0.3 is 3 out of every 10, which is 30 out of every 100, which is 30%

  VC2M5N04 | Mathematics | Mathematics Version 2.0 | Level 5 | Number

• VC2M8N03

  convert between fractions and terminating or recurring decimals, using digital tools as appropriate

  Elaborations

  • identifying when a fraction has a terminating decimal expansion from the prime factorisation of its denominator; for example, 724=0.2916_ does not have a terminating decimal expansion, while 725=0.28 does
  • identifying terminating, recurring and non-terminating decimals and choosing their appropriate representations such as 13 is represented as 0.3_

  VC2M8N03 | Mathematics | Mathematics Version 2.0 | Level 8 | Number